It's possible that the fan/light is wired with a two wire cable and someone cheated and used the bare grounding wire for the neutral. Seen it done a lot on fan/light combos that get added after the fact.

Your electrical questions might be better asked in the electrical section but it kind of sounds like you're going to be "unfinishing" your basement. Frankly I don't know how the NEC looks at that. Certainly in the "finished" portion the code is the same as in other parts of your home. For example, you need receptacles generally placed so that no point along the wall is more than 6' from a receptacle. They may also need to be arc-fault protected. Unfinished areas likely will require GFCI protection as well. Generally speaking you have to terminate wires in a junction box and the box must remain accessible. You can certainly have receptacles in the ceiling, while meeting other code requirements. If you haven't, it would be a really good idea to pull permits and have the work inspected. Municipalities are paying much more attention to this kind of stuff and not having the work permitted can cause all kinds of problems down the road.

Are we talking about the main breaker or one of the smaller branch circuit breakers? A branch circuit tripping isn't a sign of "insufficient electrical service" but just that you've plugged in an appliance too big for that circuit. Space heaters and hair dryers are notoriously heavy loads. Most residential receptacle circuits are 15A. A few are 20A for exactly this sort of reason: bathroom, laundry, kitchen, for example. You might try moving these appliances to receptacles in those spaces. Anybody who has had teenager daughters in tract houses knows the peris of them trying to run their hairdryers in the bedroom.

Internal drainage doesn't stop the water from damaging your foundation and undermining your footings. Unless there's absolutely no alternative, eg., there's only a foot between your house and a neighbouring house, it's a poor choice. Absent the known water problems, this could be taken as mild settling. Indeed, I have friends whose home leaned over several degrees but was still deemed by a structural engineer to be stable. If you're concerned, the only way to be sure is to have a structural engineer check it out.