On the bikes which have sealed bearing BB's, I replace them about every year. Cassettes likewise. Chains, at least every year, but my touring bike gets enough use that sometimes I need to replace it twice a year.
It seems, from the type of questions which you are asking, that you need to learn more about bike repair. I would suggest getting one of the "Zinn" books, as well as checking out Sheldon's site.
From what you've written, it sounds likre you probably have a worn cassette. You also sound like your chainline is not where it should be. Put the chain in the middle gear on the cogs. and middle ring. The chain should be dead straight. If not, then you have the wrong BB length for that crank.
The rings, unless defectively cast, are not the problem. It seems that the chain is compatible with your rings. Did this problem start only after you changed the chain? If so, then there's the casette issue again. Have you changed the casette? You really have to every time you change the chain on most new bikes.
Bikes are not as simple as they look.
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