Most about any gaming computer will run The Sims 3 and The computer setup you mentioned will very likely run this game. It just depends on which graphics card the setup running. The Sims 3 can be ran with a low profile graphics card so you should be able to run this game ! :D
This processor will play a big part in playing top end games yes but you will need a good graphics card also.
No, unfortunately. Not in today's world of computing. It's a single-core processor running at a slow 2.2 gigahertz. The new Celerons, however, are dual-cores, which makes them twice as efficient, and have higher clock speeds, up to 2.7 gigahertz. The Celeron E3300, E3400, and E3500 all are much better processors than the Celeron 900, and are all available for less than $65.