if I used synchronized keyword on every method of the class A will it also lock the members of the inner class as well?
No it won't.
You seem to be confused in a number of respects here.
- Using a primitive mutex (e.g. via a - synchronizedmethod) only locks against other threads that are synchronizing on the same mutex.
 
- When you call a synchronized instance method, the mutex you are acquiring is the mutex for - this... the target object.
 
- In your example, it seems that you want to lock a - staticfield, not an instance field.
 
If I understand correctly what you are trying to do, the correct way to do it is something like this:
 public synchronized int method1(){
     synchronized (B.class) {
         return x + B.y;
     }
 }
Note that this involves acquiring two mutexes, so you need to make sure that your code always acquires them in the same order.  (If you don't, then there is a risk of deadlocks.)
You would get the same effect if you created and called a synchronized static method on B for getting the value of the y field.