This is a really vague question, or set of questions. You might want to start by searching the internet to get some ideas, and then ask more specific questions once you've decided what you want.
You could search for "raspberry pi robot" or they're often known as "pibot" for short. There is boatloads of information available and loads of different designs you can use as starting points. Basically, if you're building a robot you're going to want to use some kind of motor, so you will need some kind of interfacing board between the pi and the motors. An Arduino can do this, or something like a Gertboard maybe.
One starting point might be The MagPi issue 6, which talks about the basics using an old BigTrak. Other issues of the same magazine deal with other aspects of the design as it is built up. Or you can buy a book ("PiBot: Build Your Own Raspberry Pi Powered Robot") or even buy a basic online course (same author, same title).
You might find some further ideas at let's make robots.
Yes, you're going to have to solve the power problem, presumably using some kind of battery-powered supply for the pi and all the other stuff. Yes you can use sensors, lots of different kinds. Yes you can also stream camera images if you have wifi. I don't really see why you'd want to synchronize two raspberries but for sure they can communicate with each other, probably again over wifi.