Local here, i've got the Sunday bus several times from local areas.
1. Yes you can stay overnight, that said my wife came for the Sunday and had her pillow taken by security on entry and was told she couldn't stay. I'm convinced it was some bored jobsworth, she stayed anyway but perhaps don't carry any bedding loosely.
2. Yes, see Gooner's post above
3. Yes, I believe some of these services are paid for(?) so maybe bring some cash but we've never had a problem.
Hope this helps!