When determining the total cost of a spell, you must first apply any alternate costs, then apply increases and decreases, (then Trinisphere, but that's not relevant), the spell costs you 0 as its alternate cost, then apply the arbiter's cost of 1.
I don't believe that that's necessarily true, there's no "intervening if" clause in his text, such as "At the beginning of your upkeep, if ~ is in your graveyard..." I believe that he can stack the triggers as such. Squee's ability simply resolves and does nothing while he's in play.
However, I'm not 100% because when he dies from the monument he would be a considered a different object from the source of the ability once his ability resolves.
I don't believe that that's true, the creature still has "lethal damage" marked on it until the cleanup step as the damage was from a source with deathtouch. I believe that the creature would in fact be destroyed as soon as Avacyn leaves the battlefield (once state based actions are checked)
However, I'm not 100% because when he dies from the monument he would be a considered a different object from the source of the ability once his ability resolves.