Get the data from the Firebase in limit to perform pull to refresh and load more functionality

You are missing orderByKey(). For any filtering queries you must use the ordering functions. Refer to the documentation

In your onRefresh method you need to set the limit:

 public void onRefresh() {
     // Refresh items  
     ///HERE "oldestPostId" IS THE KEY WHICH I GET THE LAST RECORDS FROM THE FIREBASE
                mChatRef.orderByKey().startAt(oldestPostId).limitToFirst(10).addListenerForSingleValueEvent(new ValueEventListener() {
.....

So the data you retrieve is the only 10 new records after you got your first 10 records.

Make sure to save the oldest key of the newly retrieved data so that on next refresh new data from this key is only retrieved.

Suggestion: Instead of adding a child value listener to find the last key, you can just use the value listener and get the last data snapshot with the size to get the last record's key.

restructure your database, set a new child id which is incremental like 0,1,2,3... etc

"chats": {
"-KZLKDF": {
  "id": 0,
  "message": "Hi",
  "name":"username"
},

then make a method for query

public void loadFromFirebase(int startValue,int endValue){

mChatRef.orderByChild(id).startAt(startValue).endAt(endValue).addListenerForSingleValueEvent(this);
}

make sure you have implemented addListenerForSingleValueEvent then do adapter related task. Initially call from onCreate method:

loadFromFirebase(0,10);

NB: loading new content in the list you have to be aware with adapter.