No, you don't.
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Downloads are sold they are not free and the Playstation Downloads that are free from the Playstation Plus are not free they require membership in Playstation Plus and expire if your Playstation Plus membership expires.
The PlayStation Portable is not considered to be a game console. It would be considered as a handheld gaming device. The PlayStation, PlayStation 2, and PlayStation 3 would all be considered game consoles.
Yes you can play PSN (playstation network) for free.
You need a license from Sony to make a Playstation Game
No the PlayStation 3 comes with Free PlayStation Network. Live is for the Xbox 360 and is not free.