1. Nope. Dominion has a number of effects, primarily influencing the scales of a province, but other than a morale modifier for potential battles it has little effect on ownership.
http://www.maladjustite.com/dominion.pdf
This document explains all. It rocks.
2. Water mages can take 1 troop with them for every magic level they have minus one.
(i.e. the first level sustains the mage itself.)
Items, thetis' blessing and the water cult theme are the traditional methods for keeping your favored landlubbers breathing.
IMHO the number of troops should be increased quite a bit. The water fringe benefit is weak, relative to the other paths. Even x5 wouldn't be outlandish.
3. There is a little symbol under the unit, with its misc. characteristics. Make sure you upgrade to the 2.08 patch, as the iconography improves quite a bit.
4. Under "Options" there is a "View Game Settings" button. For Non-Last God Standing games, data on relative progress can be viewed under Statistics ---> Score Graphs.
HTH,
Rabe the Longwinded