The rules as written aren't completely unambiguous, but their meaning can be determined.
Riots - Every player who controls a major city must roll a die, adding 1 to their roll for each troop and HQ in that territory. If your modified roll is lower than 6, remove troops equal to your natural die roll and DEMOLISH any HQs in that territory. DISCARD this card.
1) Yes, the Riots event only kills troops in Major Cities. Yes, it is possible to lose the last troop in a territory this way. (I.e. You have 2 troops + an HQ and roll a natural '2'.)
2) This is ambiguous. I would roll for each Major City independently, counting troops and HQs in each territory independently, but the rules as written state that players only roll once, and calculate their modified roll independently for each territory.
3) This is a good reason to only roll one die regardless of how many Major City territories you control and calculate individual modified rolls based upon the number of troops and HQs in independent territories. (I.e. You roll a natural '1' and have one Major City with 4 troops and an HQ in it and one Major City with 2 troops. Riots would remove the HQ and one troop from one territory and one troop from the other territory.)