1. Yes. A ground unit must choose a movmement mode, and ground movement mode that gives the unit it’s TMM requires moving at least an inch.
2. You can attack a unit with the 2/2/2, using the Swarm LRMs with the LRM1/1/1 special ability. If you hit the initial target, use the 2/2/2. If you miss, the Swarm LRMs then make a new attack on an nearby target. If that hits, use the 1/1/1.