The ongoing ‘genocide’ by ethnic Ukrainians against ethnic Russians. Unless something else presents itself, I’d say he will go with that, as he seems to talk about it more than anything else.
3 days away, so…maybe. I’m not sure if the Olympics are really factoring into his timetable, though his Chinese partners might have asked him to hold off until they are over so as not to detract from all the glory the CCP is gaining over them. 
Both I’d say. My WAG on a possible war would be the Russian start off with a huge missile and artillery bombardment, followed by airstrikes against key Ukrainian targets, then send in the troops into the currently rebelling provinces, basically annexing them into the Russian Federation to defend their populations from ‘genocide’ and at the popular demand of their adoring citizens. Depending on how that goes, the Russians might either hold tight there, or rearm and push forward to the Dnieper, maybe threaten Kyiv and try and force the Ukrainians either to negotiate away all of the captured territories or, if the Ukrainians completely fold, force them to become a puppet state in Moscow’s orbit. It will hinge, IMHO, on how well (or poorly) Ukrainians fight and how much (or little) damage they inflict on the Russians. IMHO, if it’s bloody, if the Russian’s take a substantial amount of losses, especially to big-ticket stuff like modern fighters or tanks or just a substantial number of casualties, they will hold to just the break away provinces. If they do really well…they will go for more.
No. I don’t think they want that. For a lot of reasons. First, Russia really doesn’t want to tangle with NATO or the US in any sort of fight. Putin wants…really needs…to do this with relatively little loss to his own forces. Russia really doesn’t have an over abundance of modern aircraft or MBTs or other weapons systems, and their pipeline for new stuff is very long, so replacing what he loses is not going to be quick or easy. I also don’t think the Russian people would be too keen on heavy losses these days…something where Putin goes in, grabs some land (like in the Crimea), and gets out without Russia being burned would be great. Heavy losses wouldn’t be. And if he tangles with NATO or the US Russia will take unacceptable losses. Plus, you never know where such a conflict might go.
Second, it will be more humiliating to the west if Putin rolls in and takes southeastern Ukraine and they have to sit helplessly by and watch it, especially if their sanctions don’t hit Russia as hard as many anticipate (cushioned by the Chinese).
I could see him doing this, but I think he’s got more plausible things he could or would try before something like this. There is always a risk to Putin that he would go on TV for something like this and it backfires. Even the Russians might or might not believe the US fired unprovoked on Russia…it would really be stretching things to the breaking point, especially when the US would have data that contradicts his narrative. I’d say, more plausible is Putin comes on and says Ukraine attacked Russian forces trying to aid the valiant ethnic Russians fighting to be free in the breakaway areas and Russia just has to rush in with it’s conveniently close military to save them from the vicious Ukrainians.