Correct, no auto-kill. (But Scotty is correct about the minimum 1 Thrust from bomb thrust loss, go Scotty!)
I don't see anything against it. But I think that's a "consequences of errata not fully thought out". But as currently rewritten, I don't see anything that prevents a 0 Thrust unit from attacking normally.
The move inward should replace it's normal move. Disagree with Scotty here, the rules comment on how this falling movement continues each turn, it can't happen immediately and repeatedly. It should be part of movement. Also, saying it's immediate would then lead to the assumption, since nothing says otherwise, that the unit can move during it's movement. "Units with less than 10 thrust can move one zone per turn". It would never crash. It would fall in one zone, then move out, then fall back, move out again. (Errata could say a 0 thrust unit can't move or attack except by the required falling inward each turn in the end phase, but it doesn't say that now.)
MUL template is off.