Your first question is a dup of disable f5 and browser refresh using javascript.
For your second question, it depends on what kind of application you're building, but generally, the answer is no.
If you can rely on the JS to catch the close and, e.g., send a "quit" message to the service before closing, that's easy. However, there are plenty of cases where that won't work, because the client has no way to catch the close.
If, on the other hand, you can rely on a continuous connection between the client and the service—e.g., using a WebSocket—you can just quit when the connection goes down. But usually, you can't.
Finally, if you're writing something specifically for one platform, you may be able to use OS-level information to handle the cases that JS can't. (For example, on OS X, you can attach a listener to the default NSDistributedNotificationCenter and be notified whenever Chrome quits.) But generally, you can't rely on this, and even when you can, it may still not cover 100% of the cases.
So, you need to use the same tricks that every "real" web app uses for managing sessions. For example, the client can send a keepalive every 5 minutes, and the server can quit if it doesn't get any requests for 5 minutes. (You can still have an explicit "quit" command, you just can't rely on always receiving it.) If you want more information on ways to do this, there are probably 300 questions on SO about it.
