You do NOT have to use a 20A GFCI receptacle, a 15A will be just fine. Yes, you may run the vent fan off the load side of the GFCI receptacle as long as the circuit is dedicated to that bathroom. With a 48in vanity with a sink in the middle, place receptacles on either side of the sink, approximately 2in above the backsplash and at a location that does not interfere with any mirror you may be using. Only one of these needs to be a GFCI receptacle, the other can be a standard receptacle fed from the load side of the GFCI.

Good point re the fixtures (reminds me of the Richard Pryor movie "Moving out) - it is illegal for a place to have bare wires or no fixture in place, so the place was probably sold not in compliance with local code. That may raise all sorts of legal and insurance ramifications. I agree with Shaggy if it's wired right, it shouldn't be too hard to figure out, however, I don't think the toner is the right way to go unless you're very confident and knowledgeable, most cheaper toners are signal-only so you would have to disconnect or at the least turn off the power, there are some toners that will work with mains electricity but they are more expensive. I would buy a voltmeter and test each set of wires for voltage. You may have to separate some wires to work out what's going on (you want to work out which wire supplies the power from the panel, there may be other wires attached that feed another fixture downstream. It's important to label what you take apart meaningfully, and even though it will work to have the black wire from the supply and the white wire from a different set of wires go to the fitting, you must not do so, the supply must be set up to come from the same set of wires if you know what I mean. If you are at all unsure, call an electrician. If you had a realtor working for you, you should discuss how this affects you. I can't see how it's legal if they did not leave replacement fittings, even if they were bare bulbs. If not talk to the vendor's realtor (politely and calmly) Code and legal issues aside, it's just good manners to leave things in a safe, workmanlike fashion.

The information you provided (in 2 posts) does not provide a complete and accurate picture to correctly and safely advise you on how to rewire this. Losing the pictures you took is the big problem. Not tagging each wire based on its original usage is as much of a problem. I understand you not wanting to "get someone in to do this for you". You've certainly made a mess, now, that would raise that cost significantly. At this point I can only give you a very generalized suggestion. You need to carefully figure out exactly where every wire goes and where it is wired to on the other end. Start by putting tags on each wire and label each wire with a letter and number combination. Use a letter for each cable (or conduit) and a number for the wires within that cable. To help in consistency, use number "0" for the ground wire (it will probably be a bare wire in NM or UF cable, and will be insulated green in other case) in each cable, and "1" for the wire with white insulation. The remaining wires will be "2" and higher. So wire "2" from cable "A" would be labeled "A2". Be sure they are marked in a way that cannot fall off. Take new pictures of the setup to show where each cable and wire comes out in relation to each other. Trace where every wire goes. Double check that with an ohm meter that should show near zero ohms when the wire and meter is connected to others, and near infinite ohms when not connected at the other end. Be sure every wire going into a cable is in fact coming out of that cable at the other end to be sure there are no hidden junctions you have overlooked. Then list each of these cables and wires along with their destinations, as a list and post it that way. That can make it easier for people to help you that would otherwise "have to be there to see it". Well lit close up photos at each box would help (properly commented as to what box it is). An experienced electrician would be able to do this without all this chore based on his experience helping him recognize the situations that remain after your unwiring. But it would still cost more than if he were doing it from the original still-wired-up situation. One alternative is to put everything back as you had it before and see if everything still works as it did before. Hopefully you won't burn your house down or be killed by not getting it back the way it was correctly. Sorry to be so blunt. But you got yourself into this. And maybe better wording in your post will help, too.

In the early days of GFCI, one was permitted to serve all the places it was required (bathrooms, outside). That's not been the case in several NEC revisions. As Billhart said, the bathroom receptacles must be on 20A circuits that can not be shared (they can be shared only with non-receptacle outlets in the same bathroom OR receptacles in other bathrooms, not both, anything outside the bathroom is right-out). The laundry as joed points out also needs it's own 20A circuit.