Made some changes...try this...

public class GroceryUpdate{
//VERSION 1: SORT GROCERY LIST BY CATEGORY
// PDF: INCLUDE THE Contact/Account Name
// Account Members Ages
//VERSION 2: CHANGE QUANTITY TO INTEGER TO REMOVE DECIMAL POINT
//VERSION 3: GET TYPE OF FOOD ORDER and SHOPPING NOTES FROM REQUEST (CASE)

Case request;
//Name crequest;
List <Grocery_Request__c> GRList;
List <Contact> AList;
//List <Account> atmplist;
Account aMembers;
Set<Id> GItemIdSet = new Set<Id>();
Set<Id> gIdSet = new Set<Id>();
Map<Id,wGrocery> gMap = new Map<Id,wGrocery>();
Map<Integer,Id> gSortMap = new Map<Integer,Id>();
Map<Integer,wGrocery> pdfGSortMap = new Map<Integer,wGrocery>();
Map<Id,Integer> pdfIdxMap = new Map<Id,Integer>();
List<wGrocery> gList = new List<wGrocery>();
List<Grocery_Item__c> gItemList;
List<Grocery_Item__c> pdfGItemList;
String Aid;
String AName;
// Contact c; //LG

//****************
// CONSTRUCTOR
//****************

public GroceryUpdate() {
Integer idx = 0;
Alist = new List<Contact>();
//VERSION 1: SORT BY CATEGORY AFTER WAREHOUSE ORDER
pdfGItemList = [Select g.Warehouse_Order__c, g.Name, g.Id,
g.Grocery_Category__c, g.Available__c
From Grocery_Item__c g
order by Warehouse_Order__c, Grocery_Category__c, Name ASC nulls last
limit 1000];
for (Grocery_Item__c gi : pdfGItemList) {
pdfGSortMap.put(idx,new wGrocery(gi));
pdfIdxMap.put(gi.id,idx);
idx++;
}
system.debug('@@@pdfGSortMap=' + pdfGSortMap);
system.debug('@@@pdfIdxMap=' + pdfIdxMap);

//VERSION 1: SORT BY CATEGORY AFTER AVAILABLE
gItemList = [Select g.Warehouse_Order__c, g.Name, g.Id,
g.Grocery_Category__c, g.Available__c
From Grocery_Item__c g
order by Available__c, Grocery_Category__c, Name ASC nulls last
limit 1000];

idx = 0;
String s = null;
String oldHighlight = '#BDBDBD';

for (Grocery_Item__c gi : gItemList) {
gMap.put(gi.id,new wGrocery(gi));

if (gi.Grocery_Category__c != s ) {
s=gi.Grocery_Category__c;
if (oldHighlight == null) oldHighlight = '#BDBDBD';
else oldHighlight = null;
}

gMap.get(gi.id).highlight = oldHighlight;

if (gi.Available__c == true) {
gSortMap.put(idx,gi.id);
idx++;
}
}

for (Grocery_Item__c gi : gItemList) {
if (gi.Available__c == false) {
gSortMap.put(idx,gi.id);
idx++;
}
}

//VERSION 3: GET Type_of_Food_Order__c and Shopping_List_Notes__c

//request = [Select c.Id, c.Subject, c.Contact.Name, c.ContactId, c.CaseNumber,
// c.Type_of_Food_Order__c, c.Shopping_List_Notes__c,
// (Select Id, IsDeleted, Name, Request__c, Grocery_Item__c, Quantify__c
// From Grocery_Requests__r)
// From Case c
// where id = :ApexPages.currentPage().getParameters().get('id')];

//GRList = request.Grocery_Requests__r;
//system.debug('@@@GRList=' + GRList);
//for (Grocery_Request__c GR : GRList) {
// gMap.get(GR.Grocery_Item__c).quantity = GR.Quantify__c.intValue();
// gIdSet.add(GR.Grocery_Item__c);

// pdfGSortMap.get(pdfIdxMap.get(GR.Grocery_Item__c)).quantity = GR.Quantify__c.intValue();
//}

request = [Select c.Id,c.Account.Name, c.Subject, c.Contact.Name, c.ContactId, c.CaseNumber,
c.Type_of_Food_Order__c, c.Shopping_List_Notes__c,
(Select Id, IsDeleted, Name, Request__c, Grocery_Item__c, Quantity__c
From Grocery_Requests__r)
From Case c
where id = :ApexPages.currentPage().getParameters().get('id')];
Aid=request.Account.Name;
GRList = request.Grocery_Requests__r;

system.debug('@@@GRList=' + GRList);
for (Grocery_Request__c GR : GRList) {
gMap.get(GR.Grocery_Item__c).quantity = GR.Quantity__c.intValue();
gIdSet.add(GR.Grocery_Item__c);

pdfGSortMap.get(pdfIdxMap.get(GR.Grocery_Item__c)).quantity = GR.Quantity__c.intValue();
}


//if (Aid<>){
Account[] AL=[Select a.name,(select name, age__c,Client_Status__c from Account.Contacts where Client_Status__c <>'inactive' and Client_Status__c<>'deceased' Order by Age__c desc) from Account a where id=:request.Account.Name];
if (AL.size()>0){
ANAME=AL[0].name;
if (AL[0].Contacts.size()>0){
Alist=AL[0].Contacts;
}

}






//ctmplist=[Select name,(select name,age__c from Accounts.Contacts__r) from Account where id=:request.Account];
//if (ctmplist[0].Contacts__r.size() > 0){


//}

//AList=ctmplist[0].Contacts__r;
//}


//AList=[Select name, age__c from Contact where Account like '%001E000000RoF4sIAQ%'];




//VERSION 1: GET Contact INFO
// a = [Select a.Social_Security_Number__c, a.SC_Photo_ID__c, a.Name, a.Id, LG
// From Contact a
// where id = :request.ContactId
// limit 1];

}

//**************************
// GETTER AND SETTER METHODS
//**************************

//VERSION 1: GET CONTACT INFO
//public Contact getContact(){return a;} //LG
public Case getRequest(){return request;}
public List<wGrocery> getpdfGRItemList() {
List<wGrocery> pdfGRItemList = new List<wGrocery>();
for (Integer i = 0; i<pdfGSortMap.size(); i++) {
if (pdfGSortMap.get(i).quantity > 0) pdfGRItemList.add(pdfGSortMap.get(i));

}
return pdfGRItemList;
}

public List<Name> getAList() {
return AList;
}

public string getAName(){
return AName;
}

public List<wGrocery> getGList(){
List<wGrocery> displayGList = new List<wGrocery>();
for (Integer idx = 0; idx<gSortMap.size(); idx++) {
displayGList.add(gMap.get(gSortMap.get(idx)));
}
return displayGList;
}

public void setGList(List<wGrocery> GList){
for (wGrocery gr : GList) gMap.put(gr.GI.id,gr);
}

public pageReference save() {
List<Grocery_Request__c> insertGList = new List<Grocery_Request__c>();

for (Grocery_Request__c gr : GRList) gr.Quantity__c = GMap.get(gr.Grocery_Item__c).quantity;
if (GRList.size()>0) update GRList;

for (wGrocery wGr : GMap.values()) {
if (wGr.quantity > 0 && gIdSet.contains(wGr.GI.Id)== false) {
Grocery_Request__c gr = new Grocery_Request__c(Request__c=request.id,
Grocery_Item__c=wGr.GI.Id, Quantity__c=wGr.quantity);

insertGList.add(gr);
}
}

if (insertGList.size()>0) insert insertGList;


PageReference pRef = new PageReference('/' + ApexPages.currentPage().getParameters().get('id'));
pRef.setRedirect(true);
return pRef;

}
//************
//PAGE METHODS
//************
public pageReference cancel() {

PageReference pRef = new PageReference('/' + ApexPages.currentPage().getParameters().get('id'));
pRef.setRedirect(true);
return pRef;

}
public pageReference pdfPage() {

PageReference pRef = page.GroceryUpdatePDFPage;
pRef.getParameters().put('id',ApexPages.currentPage().getParameters().get('id'));
pRef.setRedirect(true);
return pRef;

}

//WRAPPER CLASS FOR GROCERY
public class wGrocery{
public Integer quantity {get; set;}
public Grocery_Item__c GI {get; set;}
public String highlight {get;set;}

public wGrocery(Grocery_Item__c GI){
quantity = 0;
this.GI = GI;
highlight=null;
}
}

//TEST METHOD
static testMethod void T1() {
//
Grocery_Request__c qGR = [Select Id, IsDeleted, Name, Request__c, Grocery_Item__c, Quantity__c
From Grocery_Request__c
where IsDeleted = false
and Grocery_Item__c != null
limit 1];

Case qRequest = [Select c.Id,
(Select Id, IsDeleted, Name, Request__c, Grocery_Item__c, Quantity__c
From Grocery_Requests__r)
From Case c
where id = :qGR.Request__c
limit 1];

//INITIALIZE PAGE AND STANDARD CONTROLLER
PageReference pageRef = Page.GroceryUpdatePage;
Test.setCurrentPageReference(pageRef);
ApexPages.currentPage().getParameters().put('id', qRequest.Id);

GroceryUpdate stdCon = new GroceryUpdate();

Case tgetRequest = stdCon.getRequest();
List<wGrocery> tgetGList = stdCon.getGList();
stdCon.setGList(tgetGList);
List<wGrocery> tgetpdfGItemList = stdCon.getpdfGRItemList();
pageReference tpref = stdCon.save();
tpref = stdCon.cancel();
tpref = stdCon.pdfPage();
// Account tA = stdCon.getAccount();
}
}

Looks like that took, 

Error: Compile Error: Return value must be of type: LIST<Name> at line 174 column 1

//VERSION 1: GET CONTACT INFO
//public Contact getContact(){return a;} //LG
public Case getRequest(){return request;}
public List<wGrocery> getpdfGRItemList() {
List<wGrocery> pdfGRItemList = new List<wGrocery>();
for (Integer i = 0; i<pdfGSortMap.size(); i++) {
if (pdfGSortMap.get(i).quantity > 0) pdfGRItemList.add(pdfGSortMap.get(i));

}
return pdfGRItemList;
}

public List<Name> getAList() {
return AList;
}

Try this

//VERSION 1: GET CONTACT INFO
//public Contact getContact(){return a;} //LG
public Case getRequest(){return request;}
public List<wGrocery> getpdfGRItemList() {
List<wGrocery> pdfGRItemList = new List<wGrocery>();
for (Integer i = 0; i<pdfGSortMap.size(); i++) {
if (pdfGSortMap.get(i).quantity > 0) pdfGRItemList.add(pdfGSortMap.get(i));

}
return pdfGRItemList;
}

public List<Contact> getAList() {
return AList;
}

It saved, but PDF did not work, its the same?

<apex:page controller="GroceryUpdate" renderAs="pdf">
<style>
</style>

   <apex:outputText value="Grocery List for Household: {!AName}" style="font-weight:bold;"/>
   <br/>
   <br/>
   <apex:outputText value="Request Number: {!request.CaseNumber}" style="font-weight:bold;"/>
   <br/>
   <apex:outputText value="Type of Food Order: {!request.Type_of_Food_Order__c}" style="font-weight:bold;"/>
   <br/>
   <br/>
    <apex:pageBlock >
    <apex:pageBlockSection >
    <apex:pageBlockTable value="{!AList}" var="A" border="1">
        <apex:column value="{!A.Name}" headerValue="Client Name" style="width:300px;white-space:nowrap;"/>
        <apex:column value="{!A.Age__c}" headerValue="Age" style="width:50px;white-space:nowrap;"/>
            </apex:pageBlockTable>
    </apex:pageBlockSection>
    </apex:pageBlock>
   <br/>
   <apex:outputText value="Shopping List Notes: {!request.Shopping_List_Notes__c}" style="font-weight:bold;"/>
   <br/>
   <br/>

    <apex:pageBlock >
        <apex:pageBlockTable value="{!pdfGRItemList}" var="gl" id="pb" border="1">      

            <apex:column value="{!gl.GI.Name}" headerValue="Name" style="width:100px;white-space:nowrap;"/>

            <apex:column value="{!gl.quantity}" headerValue="Quantity" style="width:100px;"/>

            <apex:column value="{!gl.GI.Available__c}" headerValue="Available" style="width:100px;white-space:nowrap;"/>
                    
            <apex:column value="{!gl.GI.Warehouse_Order__c}" headerValue="Warehouse Order" style="width:100px;"/>
        </apex:pageBlockTable>
    </apex:pageBlock>
</apex:page>

By pdf did not work are you saying there is no data?

If so, it could be many reasons...the queries aren't working correctly...or the account does not have any records associated to it...or other things.

The list populates the groceries request number show up, shopping list notes will show up, but Household (Account) Name will not showup, the Clients (Contacts) related to that "Household" & their Ages fro Age__c on contact will not show up, it used to?

All of that is populated from the query that was the initial issue. Is there a custom Contact lookup for an Account? Go to the Contact Fields look for a lookup to Account that isn't a standard field. If there is one, click on it and the relationship name will be on that page.

No, the standard Account lookup filed on contact and standard lookup contact field on account (renamed Households).  The object is case (renamed request).  Standard lookups for both used on Case object no other custom lookups, the age__c is on the Contact object (renamed Clients).  The Class refers to Pages to create a grocery list that works great, once that saved you hit the pring grocery list button, the PDF comes up with the proper Grocery Lists, has the auto Case (Request) Number, The Shopping_List_Notes__c will show up, but The "Household" (Account) name is blank,  Clients (Contacts) related to Account is blank & their Age__c  (Ages) is blank, so the back warehouse who gets the PDF print out has no name, how many in house hold and their ages?