1) people believe marketing words
2) They have wanted to but the problem is not everyone runs the same hardware. You cannot get low level access unless every system is the same. This is why consoles have been able to do this for a while now already. On a PC a majority of the market doesn't have the correct GPU (GCN) so it's not going to benefit them. To me this feels like AMD couldn't bring a card to beat the GTX 780 so they need to try convincing developers to use this new API so their cards can have better performance. It's not wrong to do, but this creates problems. Developers will have to do more work. Instead of just doing a DX11 version and calling it good, they would have to do Mantle + DX11. I shouldn't say have to because no developer has to use mantle. It is likely they will be pressured to do so but many probably will not use it.
3) That's hard to say. I don't know and I doubt anyone here does, the specifics of developer relations for gaming evolved. To be perfectly honest this seems like something DICE pushed in order to make it easier to port their work between consoles. Which is ok and cool, but now AMD has to sell the other 99% of the industry that it's worth it. How do you convince Capcom, Konami, Naughty Dog (which sony owns BTW and likely won't touch anything PC so they remain exclusive), 343 industries (Halo devs who similar to Naughty Dog are owned by a console maker), Namco, Sega, Activision, UbiSoft (who has some deal with Nvidia already), Rockstar, Level 5, Square-Enix etc. that using mantle is to their benefit? Most of these developers only have a minor appreciation of PC and some of them don't care at all and never will. Outside of EA, specifically DICE and their frostbite engine nobody has signed on with this.