As stated earlier, Monuments gain favor slowly, but steadly. The bigger the monument, the more favor it generates, the more monuments you have the faster you get it etc. (There are also many different kinds of monuments such as small statues, or larger ones...obelisks all the way up to pyramids)
I'm positive that Banishing an MU will kill it. just in a "holy" sorta way. (as in, the unit doesn't die, more like dissapper/fade). I'm pretty sure that priests can't "attack" so they can't kill MUs, just "banish" them.
Interesing word to use as well