Some PlayStation games are free to download and are called demos
There are some free downloadable games, yes, but the PSN is mostly a store to purchase digital versions of games.
Owning a PSN account doesn't cost any money, and there are many free things on the PSN that you can take advantage of.
You don't get them from websites, you connect to the PSN.
The Main difference with Playstation Network or PSN over Xbox Live is that the PSN is free. PSN Plus at the same rate as Xbox Live has free games, discounts on others, online storage of your game saves, and automatic software updates to games and the console
If you buy a game on the PSN, you can delete it whenever you want - all you need to do to regain it is go back on the PSN and redownload it for free.
Yes, there are a few free games on the PSN, you can download and play games like Travel Bug, Ecolibrium and Frobisher Says! for free. PlayStation Plus members get even more free games, currently for the EU the selection includes Uncharted and Gravity Rush.
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You don't use a PC to get games from the PSN, there might be some free games released on it sometime, like Treasures of Montezuma: Blitz on PS Vita.
There might be some occasional offers on the PSN of free games. You could ask for UMDs as gifts for birthdays, or perhaps borrow them from friends.
No, PSN is free and there is no indication that is going to change.
No, you don't need to use a computer. You can connect the PSP straight to the PSN, and download games directly.
Playstation Plus subscribers get 'free' games each month, which they can play for as long as they hold an active subscription. There are a few free games already on the PSN but nothing particularly great.