Now, I read the costs and noticed each is different, do players gain problems for sleeping in "lesser" accommodations? or does it just refer to how big a room is/how much can be stores? is it weekly? or nightly? or up to GM?

Seems to me to be more of a roleplay thing. I imagine a nobleborn character might scoff at staying at Roach Accomodations+. Also, I suppose if you're feeling especially nasty, you could knock off less fatigue for sleeping on less comfortable accomodations but I don't think there's a substantial difference outside of roleplay opportunities.

What ColArana said. Though you could also throw in some improvised mechanics if you want to, such as forcing a Toughness test because the room was unheated and/or wet and people might get sick (for -5 temporary characteristics damage), or because the food sucks. Or maybe it's not as secure and there's a risk of a thief trying to steal from them.

Is the cost nightly? or Weekly? or is it generally up to GM? I know I could Rule 0 it, as the game suggests but, I was curious if it's nightly or weekly.