What could be causing these to happen

So Im trying to fix these brake lights, Ive never traced a wire problem in a car, but I got a multimeter, how do I read an electrical diagram and find the source of my problem? Ive fixed parts related to the problem but I think its a wire, Im tracing wires, any tips? thanks :)

I had the new altenator checked and it was good but it was not charging the battery. If it is not the alt or the battery what could be causing this to happen

Towed to mechanic who estimated $500+ to repair. Could I do this repair myself? ? I found a new, complete set of part (s) online. Any other possible causes? Oh yes, it sometimes hesitates, or engine just stops at red lights or even when driving slowly. Odd. Any ideas for me?

when I stop, the car in drive. I shift to N and it stops. At one point I excelerated to quickly and the car stopped. Glad it turned right back on when I started it. The rear light warning also comes on when I shift into gear. The mech that installed the ALT. says the engine has seen its day. I think he's seen his dad. I think he didn't tighten the belts enough. Can you please advise? Thank you so much!

Also if you can describe what it looks like. I've seen a squared shaped and a round cylinder shaped one as well. I'm having issues with the blower not coming on with both the air or heat settings being on.

I can not find the problem with this car runs good at idle runs rough when at higher rpms codes are 12,13,14,16,21,22,24,25,26,27,31,32,41,42,43,51,71,99 and codes will not clear I have no check engine light this one has me wondering

This is the first time this has happened and is that a leak in the gas line

The rear running lights stopped working on my car. But the brake lights still work. Usually a light comes on in dash when a light is blown and I've not seen it yet and the bulbs look fine. Is there a fuse I need to check and change?