As a quick note, the game does not really have full cover or half cover. We used to have it, but it was proving too difficult to see what types of obstacle gave what (as you note). What we do have (and what I think you're seeing) is cover and blocked line of sight. If you run up to a large rock, you can still shoot over it, so you're in cover. If you run up to a large tree, you cannot shoot through it at all (you also cannot be shot at).
As for the other thing, I think there are 8 special defense modes (so 9 including the normal one). They all make a unit harder to hit, but the special ones do other things too (hyper armor gives more armor, others might give the unit regeneration or shields). The system does support each one giving a different icon, but I would worry that the icons are too small to really communicate what the differences were, so I'm not sure how useful it would be.
As for the other thing, I think there are 8 special defense modes (so 9 including the normal one). They all make a unit harder to hit, but the special ones do other things too (hyper armor gives more armor, others might give the unit regeneration or shields). The system does support each one giving a different icon, but I would worry that the icons are too small to really communicate what the differences were, so I'm not sure how useful it would be.