Prevent any form of page refresh using jQuery/Javascript

#1 can be implemented via window.onbeforeunload.

For example:

<script type="text/javascript">
    window.onbeforeunload = function() {
        return "Dude, are you sure you want to leave? Think of the kittens!";
    }
</script>

The user will be prompted with the message, and given an option to stay on the page or continue on their way. This is becoming more common. Stack Overflow does this if you try to navigate away from a page while you are typing a post. You can't completely stop the user from reloading, but you can make it sound real scary if they do.

#2 is more or less impossible. Even if you tracked sessions and user logins, you still wouldn't be able to guarantee that you were detecting a second tab correctly. For example, maybe I have one window open, then close it. Now I open a new window. You would likely detect that as a second tab, even though I already closed the first one. Now your user can't access the first window because they closed it, and they can't access the second window because you're denying them.

In fact, my bank's online system tries real hard to do #2, and the situation described above happens all the time. I usually have to wait until the server-side session expires before I can use the banking system again.

You can't prevent the user from refreshing, nor should you really be trying. You should go back to why you need this solution, what's the root problem here?. Start there and find a different way to go about solving the problem. Perhaps is you elaborated on why you think you need to do this it would help in finding such a solution.

Breaking fundamental browser features is never a good idea, over 99.999999999% of the internet works and refreshes with F5, this is an expectation of the user, one you shouldn't break.