Can Band of Misfits be played as a reaction card?
No, you can't play it as a reaction card. Only cards labeled "Reaction" on the bottom can be played as reactions. Band of Misfits just says Action, so it may only be played during your turn.

When you do play it during your turn, if Moat is in the supply, you can certainly play it as a Moat, to get +2 Cards. But it doesn't copy another card until you actually play it, and you can't play it except as an action during your own turn, so you can't use it to get the protection from attack that Moat offers. When someone else plays an attack card, you have no opportunity to play an action card, so you can't play Band of Misfits then.