0ihor It's possible your Steam CD Key was auto-consumed when you linked your accounts, which isn't required in order to play Sims 3 through Steam. I can't prove that's true, but regardless, the key isn't working on the Store site and it's not going to. If you can't use the Store to download content from the Exchange, or free content like Riverview, that's a problem (not a bug) that EA customer support should be able to help with, for example by adding the game to your account again.
However, the free SimPoints offer stopped working some time ago and hasn't been fixed, and probably won't be fixed in the future. Here's the master thread if you're interested:
Redeem free simspoint on Thesims3.com | EA Forums - 11166085