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I'm not too savy on the PC end of things, so I don't know if you would be able to set up a media center pc the way you described with multiple inputs and have it output multiple sources simultaneously, but the home theater end of stuff I'm a wizz at.
Most standard A/V equipment is only designed to work as a single output source so you are going to have to get in to home integration stuff if you really want it to work the way you described. Either that or buy a ton a gear and make a "home run" where everything is located. There are home networking hubs that will allow you the integrate an entire home theater system through one centralize unit, but you are talking some serious cash. Verizon has solved this problem with their media center dvr boxes. You can record stuff on one box and send it to any other box in the house, but FIOS is in such a small percentage of the country that you probably wouldn't be able to take advantage.
The remotes are easy enough. If you have the ability to run cat-5 though the house you can set up an IR repeater system. If not you can set up a RF based system. Any decent universal remote will have the ability to do both and you can set up the signal to eliminate any cross talk or interference. So you can have a remote that will operate just the bedroom and one that will operate just the living room and have them both working the same system. Any decent a/v store will be able to walk you through it or have an install crew that can set it up no problem (just avoid best buy and circuit, they are usually clueless)