An unhandled exception moves up the method stack in search of a matching When an exception is thrown from a code which is wrapped in a try block followed by one or more catch blocks, a search is made for matching catch block. If a matching type is found then that block will be invoked. If a matching type is not found then the exception moves up the method stack and reaches the caller method.
Same procedure is repeated if the caller method is included in a try catch block. This process continues until a catch block handling the appropriate type of exception is found. If it does not find such a block then finally the program terminates.

There are two ways to handle exceptions,
1. By wrapping the desired code in a try block followed by a catch block to catch the exceptions. and
2. List the desired exceptions in the throws clause of the method and let the caller of the method hadle those exceptions.

It is not necessary that each try block must be followed by a catch block. It should be followed by either a catch block or a finally block. And whatever exceptions are likely to be thrown should be declared in the throws clause of the method.

Yes even if you write return as the last statement in the try block and no exception occurs, the finally block will execute. The finally block will execute and then the control return.

No. In this case the finally block will not execute because when you say System.exit(0); the control immediately goes out of the program, and thus finally never executes.