Can you connect a router into a network that uses a switch?
The answer is yes. If you need more information, please be more specific on what it is you're trying to do.
Yes. Generally you plug your internet connection into the router, then an ethernet wire from the router to the switch. More than likely, depending on what set-up you previously had, your going to have to change your tcp/ip settings. I could probably guess what set-up you have... but you'll have to be more specific before we can give more advice.