Every time the critter's Action Phase comes up, the critter automatically inflicts damage with a base DV equal to its Magic attribute. Net hits on the melee attack increase the DV of this damage. The victim resists this damage normally with a Damage Resistance Test, using Body + half Impact armor (round up_ unless otherwise noted.
Emphasis mine.
As you noted, the damage happens automatically, without effort on the critter's part. So he doesn't re-roll the damage every round. The damage is, as stated, Magic + Net Hits from the original melee attack. So it's 7S every round in your example (resisted with Body + half Impact).
Your second question is iffy-er. Officially, you have the following:
Engulfed victims may not move.
GM interpretation could go either way, nothing stops the engulfer from moving, but since the engulfee, per RAW, may not move, then the GM may read that as saying that if the engulfer moves, the engulfee is left behind.
Don't forget, the engulf power draws the victim into the critter
or terrain it controls (SR4A, pg. 294, Engulf). So, you can drag the engulfee into a lake instead of the water elemental itself. Then he's stuck AND the spirit is clearly free to move.