Yes, I'd recommend Amazon or play.com. Perhaps even eBay if you trust it. Walmart.com has some at 2 for 30 and also sells some used. Many sites sell the games, some you can get downloads from PlayStation Network.
I also suggest TheHut, Planetaxel or PlayAsia.
The only site for PS3 downloads is the PlayStation Store, which has exclusive rights to PS3 game downloads. The online sites can only be used to order game discs and not game downloads
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If by online games you mean online multi-player than yes
Some PS3 games have online play. When you own the game, have an online connection, and the game disc is in the machine you can play online
Some PS3 games have online play. When you own the game, have an online connection, and the game disc is in the machine you can play online
At this time you can not, you must go to the PlayStation Store to buy games
No the PS3 network is free to play games on