My wife and I currently live in an apartment. Equipment storage is a serious issue, among other things. I have a quite large closet dedicated for brewing stuff, however, when I need something, a lot of the other "stuff" has to come out for me to get to it.
The city water supply sucks.
I have to mash in the kitchen or dining room when its really cold outside. I boil with a turkey fryer on a 5'x10' wooden deck that I'm not supposed to have a propane burner on. Chill in the kitchen with an adapter for the sink faucet.
I love brewing too much to let it slow me down, and I have to say that the quality of my beer has improved a TON since moving to all grain last March and reading, reading, reading.
We'll be moving soon--into a house---and I'll hopefully have room to spread out a bit!
About your trub waste in the kettle-
I have recently accepted that I am going to be throwing out some wort. You have to leave it behind somewhere and I figured I would leave it in the kettle instead of the primary. In the past I have dumped all the trub in the fermenter. I don't know what in my mindset happened, but there is something awesome about crystal clear wort going into the fermenter. I have upped my recipes a little to account for more waste. Pennies, maybe dollars more for cost...not much.