Hi,

There are quite a few issues here:

1. on Responses__c (before update,after insert, after delete) - Why is is that you want to do this "before" update but "after" for insert and delete ?
Generally, if we are updating another object, we should do it in "after trigger" so I would change "before update" to "after update"

2.  if(trigger.isinsert && trigger.isbefore && trigger.isupdate) - This will NEVER be true so that block of code will not execute at all.  I think you need to change this to : if(trigger.isafter && (trigger.isinsert || trigger.isupdate))

3. mapcam is a map of the object Responses__c.
So, the statment "select id, CampaignId, Contactid, Status from CampaignMember where CampaignId in : mapcam.keyset()" is incorrect because you are trying to get records from the CampaignMember records using a list of Responses__c ids.
you need to collect the campaignids from the Response__c objects into a list or set and use that to query against CampaignMember like this:
Set<Id> setCampaignIds = new Set<Id>();
for(Response__c resp : trigger.new)
{
   setCampaignIds.add(resp.CampaignId__c); // or whatever that lookup field is called in your response__c object
}
list<CampaignMember> cam = [select id, CampaignId, Contactid, Status from CampaignMember where CampaignId in : setCampaignIds];

You need to do something similar for deletes as well.

4. You are performing this on every insert/update/delete.  For update, it would be a good idea to check if the Status or Contact field has actually changed

5. The for loop has an insert inside it and update outside it.  I am not sure what you are trying to do there.  You should not be inserting the list of CampaignMember records every time you add one to the list.

for(CampaignMember c : cam){
   c.Status = mapcam.get(c.Id).Response_Status__c;
  // c.SystemModstamp = mapcam.get(c.Id).LastModifiedDate;
   resp.add(c);
   
   insert resp;

  }
  update resp;

Hope this gives you enough to get started