No it is not unusual to have banks make you pre-qualify with them, as I am seeing more and more relocation companies do the same thing.
They want to assure themselves that the deal will not fall through over financing. Go ahead and do it, you c an still use your own lender. No, it is not unusual for banks to take a LONG time to respond. They are really not in the RE buisness and now are having to juggle a lot of homes to sell. Unfortunately, when you deal with bank properties, they don't care about YOU. They just want to sell if for the best price with the least amount of conditions. If this is the house you want, you just have to be patient.
"as is" means exactly that. If you are concerned, do a inspection before the offer is accepted so you know any defects. Some, ( very few ) will do repaires, most do not.
However, If you really want this home, remember the cleanest offer will win out.