Units darken at low health, though when health is barely more than the opponent's attack, that effect may be hard to notice.
Health does indicate a unit's max health.
Heal heals adjacent units (if a unit 'walks' into a wounded unit, it heals it).
Regen heals units passively when they neither attack nor heal (so, when units move or stay in place, they regenerate health based on the Regen stat).
Convert can't give more health than Health (so, its effect caps at [Health]).
I might add some clarifications, a sort of rule book, in the future, as I've been asked these questions a few times already.
Also, if you play on mobile, I recommend switching to laptop, as the controls are better.
Tip (skip if you don't want): With these stats, I'd expect you die pretty fast (because enemy units kill your fighters in two hits). With some more health, you'll be better able to surround effectively. I might add hints in the future when a player should probably invest more in critical stats.