ofcourse you can call thread.sleep in synchronized 
block,when we call means when there is a possibility of 
loop inside the synchronized block.

While the thread is sleeping in a synchronised block means, 
you are locking a resource, there might be 'n' number of 
contenders for this resources. If the thread goes to sleep 
then other threads or processes contending for the resource 
will be blocked infinitely.

yes, you can call wait method inside synchronized block but 
synchronized block usually allows one by one to penetrate 
in.if you call wait method inside it will create a stagnant 
circumstance. synchronized block wont allow other threads 
inside till this thread in waiting state get notified

Yes we can call,And should be enclosed between try catch 
blocks beacause Interupted exception may be thrown.