You are correct, the SQLs in the FOR loop is the issue.

Its a little complex, but basically you need to get the record Lists using the Ids.  Basically, loop the records, get the Ids, do a query (outside the loop) using Ids IN :listOfIds, then loop that list to create another list of Ids, and do the next query, outside the loop.

The following is uncompiled and not tested, but I think it should get you on the correct path:

trigger closeCaseOnIcmDischarge on Patient_Ass__c (After insert) {
    
    Set<Id> pavIds = new Set<Id>();
    List<Patient_Assessment_View__c> pavList = new List<Patient_Assessment_View__c>();

    for(Patient_ass__c pAss : trigger.new){
        pavIds.add(pAss.Patient_Assessment_View__c);
    }
    
    Patient_Assessment_View__c pView = [Select id,Account__c
                                             From Patient_Assessment_View__C
                                             Where id IN :pavIds]; 
    Map<Id,Patient_Assessment_View__c> pViewMap = new Map<Id, Patient_Assessment_View__c>();
    Set<Id> AccountIds = new Set<Id>();
    for( Patient_Assessment_View__c pv : pView ){
        pViewMap.put(pv.Id, pv);
        AccountIds.add(pv.Account__c);
    }

     List <Case> cases = [Select id, Discharge_Reason__c, Discharge_Date__c, Accountid
                   From Case
                   Where status IN('New','On Service')
                   AND RecordTypeId = '01236000000OJLq'
                   And Accountid IN :AccountIds];   
    Map<Id,Case> caseByAccIdMap = new Map<Id,Case>();
    for (Case c : cases ){
        caseByAccIdMap.put(c.AccountId, c);
    }
        
     List <TeleWell_Care_Plan__c> TWs = [Select id,Use_Question_1__c
                                  From Telewell_Care_Plan__c
                                  Where Patient_Assessment_and_Care_Plan__c IN :pavIds] ;

    Map<Id,TeleWell_Care_Plan__c> carePlanByPAVidMap = new Map<Id,TeleWell_Care_Plan__c>();
    for(TeleWell_Care_Plan__c tw : TWs ) {
      carePlanByPAVidMap.put(tw.Patient_Assessment_and_Care_Plan__c, tw);
    }

	List<Case> updateCases = new List<Case>();
    List<TeleWell_Care_Plan__c> updateTWs = new List<TeleWell_Care_Plan__c>();

    for(Patient_ass__c pAss : trigger.new){
	String accId = pViewMap.get(pAss.Id).Account__c;

        Case tempCase = caseByAccIdMap.get(accId);

        if(!Isnull(tempCase) && pAss.RecordTypeId == '01236000000nufHAAQ'){
        tempCase.get(0).status ='Closed';
        tempCase.get(0).Discharge_Reason__c = pAss.Discharge_Reason__c;
        tempCase.get(0).Discharge_Date__c = System.today();
	updateCases.add(tempCase);
             
        }    
    }
    update updateCases;

    for(TeleWell_Care_Plan__c tw: TWs){
        tw.User_question_1__c = 'No';
        updateTWs.add(tw);
    }
    update updateTWs;
}

Note that also you were doing DML events inside the Loops also, which would also breach the governor limits.  For those, add the records to be updated to a list of records, and then update that entire list in one call outside the loop.

Regards

Andrew