And after giving a team to move, if they get under fire by so little as one shot, they take cover and abandon the given order. After the first round shot at them, you could at least in previously versions of CC, give them the new command and they would continue to move even if shot at again. In pitf i tend to see that they stop and defend/ambush, every time they get shot at, more or less. I don't like that.
The code for this behavior hasn't changed from previous versions of CC. A team that is not under fire will usually stop and head for cover when it first takes fire. You can order them to continue moving while under fire, and they will usually do it, but it depends on the team's morale and experience, and the movement order you use. For best results use a short 'Move Fast' order.
A team LOS line for a team is drawn from the gunner for dedicated heavy weapons teams like HMGs and mortars, but not for infantry teams that happen to have an LMG. Positioning the gunner in these teams can be tricky during deployment, due to the way 'rifle' type infantry teams are handled in the engine. But you can use a movement order to reposition the team and the man with the LMG should go right to (or right next to) where you put the destination dot.