Amiibos are just bots.  You can level them up by playing against or with them.  Thats it.  Also, they probably have to be from the correct amiibo line in order to level them up, otherwise they will probably just show up as a computer bot... For example, if you try using a mario kart amiibo in smash bros, you will only have access to a basic mario character, devoid of any of the smash amiibo features...

I do wonder how long before Sony tries to introduce a line of gaming-compatible figurines.

The interaction of the figurines with the games is very limited with Amiibo. It's actually pretty useless. So far it doesn't unlock any characters which should be the whole point. It's just a cool looking memory card as of right now. And besides, Disney characters are far more recognizable than Nintendo characters. So parents who shop for gifts will be more drawn towards Disney Infinity because their girl loved Frozen and their boy loved Cars.

Nintendo characters are not bigger than Disney characters, barring Mario and Pikachu.

I don't know, but I will be collecting them. I couldn't care less about Disney stuff though.

Speaking of which Infinity 2.0 is coming out before Amiibo.

they need to:
cut wii U price.
make compatible also with old games(pikmin, DKCTF, mk8)
release a new 3ds version with nfc included.

As a huge Nintendo fan, I honestly don't think Amiibo will do as good as many think. It think its a neat concept but the in-game concept of the game isn't really clear and I feel like they should have introduced them in a game centric around using the Amiibo's. There's no real convincing reason why I need an Amiibo.

It will flop sooo hard...unless they don't make it cheap, and I seriously doubt it considering how they usually overprice their hardware.

sure, like they did with Wii, Gamecube and DS