I don't know if it does, but I live in Europe so that is not an issue for me.
Does it run a modern version of Android?
4.2.1
Does it have a modern SoC
It has more than enough horsepowers for what I do on a smartphone. It's quad-core, as for details - I never bothered.
Is it widely available in the US? Can I get after sales support?
Again, I don't know much about US, but I would imagine that a big company like Lenovo would be present there in one form or another.