85 Volvo 245 DL wagon.
Car completely died on me while driving. No lights, no accessories, no nothing.

I've been having starting issues with the car ever since a really amateur backyard mechanic put an exhaust on for me.
At first we had to jiggle the wires under the shift boot arbitrarily, and then it would start.
Then it wouldn't start at all unless I jumped it and let it run for a half hour or so.
Now it's completely toast.

There are numerous wires that I've found that are exposed, and I've taped them up as a temporary fix.
Battery/alternator test perfectly fine with the multimeter.
Cleaned fuse terminals and battery terminals. Checked battery ground, it's fine.
One fuse always blows after the car runs for a few minutes, another fuse keeps my taillights permanently on unless I take it out.


What should I do?
I'm really confused here and don't have thousands of dollars to spend at a shop. Where should I start looking/diagnosing? What tests could I perform at home to try and isolate the problem?