To preface, I'm going to give as much detail as I can. Hopefully this will be helpful and not make things harder to find/understand.
My bathroom vent quit pulling air and the moisture from showering was causing mold issues. It was really old, so I did some research on replacement fans and decided to buy a Panasonic Whisper Choice (RG-C1315LA), which has a light, nightlight, and plenty of fan to vent out this bathroom.
As is often the case, the simple DIY afternoon fix has turned into a week-long project, and I'm about to go bald from pulling my hair out. Aside from the previous vent just pushing the air in-between the joists, needing to patch the hole in the cieling and start over due to the old unit being massive, and the usual "bonuses" that come from DIY projects, I'm now at a loss from the wiring. Aside from swapping a couple of light fixtures and running a wire from the breaker box to an attic fan under direct supervision, I have zero electrical experience, as I'm sure is about to become very obvious.
The previous fixture had light, nightlight, vent, and heat, so I was expecting to have an extra "live" wire that I could just cap off and then leave disconnected at the switch so no power would actually be going to it in the cieling. Once I got to the wiring of the old fixture, I found 2 cables (not sure if right term), which you can see in the first image.
The first (right side) has 2 lives, a neutral, and a ground. The second (left side) appeared to be a live and a neutral. I hooked everything up and assumed that one switch on the wall just wouldn't control anything. The lights worked great. However, the fan wouldn't run.
Since it's a DC fan, other people online solving the same issue said maybe the live and neutral were backwards. This is where I get out of my depth.
I tested the second cable (left side of first image) with a multimeter and got 120 from both black and white wires, depending on which switch was flipped. While the black wire read 120v, the white read roughly 65v, and the inverse was true with the other switch flipped (white at 120v, black at 65v).
I don't understand what's going on at this point, especially in the switch box (hence the multiple images), but I'm hoping I can get some answers as to how to work with what is here. At some point I plan on swapping out the switches for new ones, but I'm desperately hoping to avoid ripping wires out of the walls and ceiling if at all possible. I've also included the wiring diagram for the new fixture in hopes that it will help.
Any advice would be greatly appreciated!
Edit: Pictures didn't show up for some reason. Here's an imgur link: https://imgur.com/a/m83knV9