There is a game on facebook called Sims Social not as fun but it's similar. :)
Can I Play The Sims 3 Online Without Buying The Game?
I'm not so sure about playing it online but, you could keep looking. What I suggest you do is download the game to your cpu and ask a friend for the serial key. That's what my sister did.
No no you can't
Yes you can I did it before and it works
No, You can't play The Sims 3 Online for free because you have to buy it unless you use someone's or download it. Downloading it is illegal it's like a bootleg of the game.
Play online for free