The answer is, "It depends." Some of your apps may run without modification on WM6, while others may require an update, and some may not work at all. You might want to contact the individual developers regarding compatibility questions.
You should not have to pay a second time to move your apps to the new WM device, as long as you delete them from the old device (for legal reasons). However, if you need an update to your program for compatibility, it is up to the developer whether or not they charge for updates.