Correct me if I'm wrong, but you have your modem in another room, where you get 110 Mbps, and then you have a wired connection to your room where you only get 42Mbps?

Well, to answer your question in the edit, no degradation is supposed to happen over 100 ft of cable. Maybe it's wired wrong, I would get a cheap cable tester to make sure there aren't any crossed wires.

For Tone gen, Fluke makes the gold standard. They also have a cheaper version. You didn't mention a probe, so maybe you are looking for a cable certifier?. That's super expensive though. if you just have to test that there is continuity and not certify the cables, you can use this, or this if you want to look like a pro.

As for Screwdrivers, Wiha makes the best screw drivers, hands down. I have this set for working on electronics & laptop repair. Magnetic tool-kits are fine. This isn't the 80's anymore. There aren't too many magnetically sensitive items inside a computer anymore. especially with the advent of SSD drives.

As for a toolbox, depending the work, I prefer a tool bag or pouch.

Good luck, hope that helps. What helped for me when I started was to go to harbor freight and just get an assortment of tools. As I worked I slowly replaced the stuff I used all the time with quality gear, and didn't have to burn myself buying expensive tools and gear that I would never use.