1) A unit in Red is a dead unit during combat. If the unit is in white, it has been suppressed, and will no longer participate in hurting the enemy, but can still be taken as losses. If the whole unit is panicked, the attacker will get a bonus in shooting at it, so more of them will die.
2) Integrity is the health bar. It essentially just shows how much of the unit is left from full strength.
3) You can put any unit into any HQ wherever you want. However, if they are in combat, they will get the HQ bonus if they are with 5 hexes of it. If the unit is not going to fight (like your Romanians on Coast watch) then it doesn't matter where the HQ is (if/until the enemy lands near them)
“My logisticians are a humorless lot … they know if my campaign fails, they are the first ones I will slay.” – Alexander the Great