Hi All,
I need to send email messeges to my contacts on closing the cases also need to create Task and Email Messages record. I have done some thing like this.

trigger sendemailonclosecase on Case (before update, after update ) {

Set<Id> Caseidset = new Set<Id>();
List<Case> updCase = new List<Case>();
List<Case> Caselist = new List<Case>();
Set<id> conidset = new set<Id>();
List<Messaging.SingleEmailMessage> msgList= new List<Messaging.SingleEmailMessage>();
String [] emails = new List<String>();
Map<Id, String> Emailmap = new Map<Id, String>();
Map<Id, String> Accountmap = new Map<id, String>();
List<Task> Tasklist = new List<Task>();
List<Emailmessage> ListEmail = new List<EmailMessage>();
if(trigger.isAfter){
        if(trigger.isUpdate){
            
        System.Debug('>>>>>');

EmailTemplate et = [Select Id from Emailtemplate where Name = 'closurecaseemailtemplatece1'];
            for (case c : trigger.new){
                        if(c.status == 'Closed' && c.Survey_Sent__c == false){
                    conidset.add(c.contactid);
                                        }
                                        }
                    List<Contact> contactList = [Select Id, Email, AccountId, Account.name from Contact where Id In: conidset];
                    for(Contact ct : contactList){
                            Emailmap.put(ct.Id, ct.Email);
                            Accountmap.put(ct.AccountId, ct.Account.Name);
                            }
                    System.Debug('>>>' + Emailmap);                               
                    System.Debug('>>>' + conidset);
                    System.Debug('>>>' + Accountmap);
                            for(Case cCase : Trigger.new){
                                   System.Debug('>>> for cas');
                                    if(cCase.Status == 'Closed'){
                                            System.Debug('>>> if' + cCase.status);
                                        Messaging.SingleEmailMessage msg = new Messaging.SingleEmailMessage();
                                        msg.setTemplateId(et.id);
                            msg.setTargetObjectId(cCase.ContactId);
                            msg.setTemplateId(et.id);
                            msg.setWhatId(cCase.id);
                            msg.setSaveAsActivity(false);
                            if(!Emailmap.isEmpty()){
                            emails.add(Emailmap.get(cCase.contactId));
                            }
                                System.Debug('Sting' + emails);
                                if(Emails.size() > 0){
                            msg.setToAddresses(emails);
                            }
                            msglist.add(msg);
                            // Updating Case hear-------------
                                //cCase.Survey_Sent__c = true;
                                Caseidset.add(cCase.Id);
                            // Creating Task hear ------------
                            Tasklist.add(new Task(ownerId = cCase.OwnerId, Priority = 'Normal', 
                                                Subject = 'Case ' + cCase.Casenumber + 'has been closed', whoId = cCase.ContactId, WhatId = cCase.Id, Account_Name__c = Accountmap.get(cCase.AccountId)));
                            System.Debug('>>> ' + Tasklist); 
                            ListEmail.add(new Emailmessage(FromName = 'FXAll Client Service',
                    ToAddress = Emailmap.get(cCase.ContactId),
                    Subject = 'Case ' + cCase.Casenumber + 'has been closed',
                    TextBody = 'Thank you for contacting AM3CS your Case ' + cCase.Casenumber + 'has been closed',
                    ParentId = cCase.Id, 
                    ActivityId = Tasklist[0].Id));
                    System.Debug('>>> ' + ListEmail);
}
}
Messaging.sendEmail(msgList);
           
Insert Tasklist;
Insert ListEmail;
}
}
/*updCase = [Select Survey_Sent__c from case where Id IN : caseidset];
                       for(case c : updCase){
                               c.survey_sent__c = true;
                                   Caselist.add(c);
                                   }
                                   
                                        
Update Caselist;*/
}

Hear I am getting Activity id null and if my email has been sent I want to update my case with survey_sent__c = true. I am not able to update case records may be i am doing something wrong i have commented the code for this.
Also I need to do some other modifications. we have 5 customer email addreses where we receive cases, I wants to send different email templates according different customers email addresses like if we receive case on customer email address1, template1 should be sent and accordingly.
Please suggest how can i update the case records and achieve this functionality.
Thank You