I always prepare my cases before I tumble them, but, that's just me.
resize, deprime, expand case neck, clean primer pocket, dump in tumbler.
I like to have them ready to load when they come out of the tumbler, and if I don't resize them first they get all yucky after tumbled when I chuck them up in the die.
2) The tumbling will take care of the inside, (as much as can be taken care of anyway), they won't be all shiny inside, if that's what you mean.
3) The dampness probably won't hurt anything, I wouldn't think after a week anyway. The tumbler media should soak all that up.
*Note* This is the way I do it. This isn't a "standard" or anything, the only thing wrong with MY way (that I can see) is when you deprime first, you have to poke the little pieces of tumbler media out of the flash holes as you take the brass out of the tumbler.
However, when it's cleaned up, it's ready to load. To each his own I guess.