1 - Lots of the latest games are mutliformat and appear on both the 360 and PS3. However there are games like the Halo series, Gears of War & Fable which are 360 exclusive. Personally I prefer the 360's exclusives but it's really a matter of taste.
2 - Yep, you can play online on the PS3, and the PS Network is free. You have to pay for Xbox Live but it is the superior service in most people's eyes.
3 - The Wii is a very social console. Stuff like Wii Fit & Wii Sports are great with family and friends. However the other consoles also have social games like the Singstar and Buzz games on PS3 or Scene it? and the upcoming Lips on 360.
4 - Nintendo has a unique style which most experienced gamers love, but they are making less core games these days. Mario Galaxy is one of the best games ever made and is Wii exclusive. Mario Kart is available on Wii and is good too.
I'm a 360 gamer mainly but my daughter has a Wii and it is a good console. With my impartial hat on i'd say go for a Wii to compliment your PS3, as it really does offer something different to what you already have, and is great in a social environment.
Good luck choosing though mate.