On a picture I'm looking at of the fuel pump + sender assembly, there are two connectors. I'm not very familiar with that circuit but I suspect that one goes into the tank for pump power and fuel level sensing from the sender, and the other goes to the evaporative emissions cannister above the spare tire.
I may be wrong! Anyway, are you stating that the box with wires coming off, has them disconnected or that it terminates in a plug and is plugged into something? It is hard to imagin that someone competent replaced the fuel pump and left something like that in disarray, and yet, apparently they did if they are being honest and all those things seemed to go wrong after the fuel pump replacement.
Anyway, there are no inline fuses that I'm aware of, so did you check the fuse box for blown fuses?
The instrument panel lights could be a fuse, or a broken wire or bad connector, or they could be a crack in the instrument panel circuit board. This becomes an issue of how much you trust the seller to give you the truth instead of underplaying problems and acting as though all will be easily fixed to make a quick sale.
Some of these issues, especially your wipers only working on high speed, are either a bad relay or the GEM module has partially failed. Consult your owners manual for the wiper relay locations. There are two of them, one controls power to it and the other switches it from high to other modes, "IF" I recall correctly. You can swap an identical relay from another location in the relay box with the suspect one to see if the wipers then work and/or the other circuit you swapped a relay from, still works as a sign the relay is okay.
All of this at once is really too much to try to handle in a single forum topic so I'm linking to more info including a schematic of the wiper circuit and a fellow owner that seemed to come to the conclusion that his GEM was bad: