My answer is to the question “Is it possible to exhaust this card and, instead of removing two runes, remove 4 runes and do 2 damage”, I hope I have understood you correctly.
Answer: No. I do not see anything on the card that would allow you to do that. The ability is “exhaust and remove 2 runes” to “deal 1 damage”. Otherwise, the wording would be different (something like: Exhaust this card => Remove an even number of blood runes from this units, for every 2 removed, deal one damage …)
- Yes, the coin cost can be repeated unless otherwise specified. There is nothing in the rules that prohibit you from repeated use of an ability unless otherwise noted on the card or by rules of the costs involved.
- Yes. The rules are very clear about the fact that arrival fatigue (see below) only applies actions/abilities that require exhausting.
- Yes, in each instance you have the choice of paying coin of exhausting the unit. Naturally, for exhausting the unit, it may not suffer from arrival fatigue and may not be exhausted already.
In the rules (version 46), on page 17 it says: “All card types have arrival fatigue, which means the turn they come under your control, they can’t use abilities that require exhausting as part of the cost. If they are units or heroes, it means they also can’t attack the turn they come under your control. If a card has haste though, it CAN attack and use exhaust abilities the turn it comes under you control.”
I hope this helps