2) Pretty much, however Ice Burners only appear during certain event periods. Right now you can't buy them from the cash shop, so expect prices to increase in the market for them (ice fragments). Also it's not really worth it to get the boxes, since you can find them later (and quite easily), or buy them cheaper from the market.
4) Theres a difference between berserk and awaken. Only the boss that we discussed can go into "berserk" form, where it opens its mouth, gains more hp and generally is more annoying. This happens when the other two parts die.
Bosses can awaken much like you can with CTRL. Pretty much all bosses can do this I think, where it suddenly counters your attack and deals 1 damage to you, knocking you down. The boss turns red, and gains Super Armour for a short period of time (cannot flinch or be knocked down), and deals more damage.