If you're interested, you can learn enough to follow along by watching a lot of YouTube videos. I don't think it would be practical to explain all of the background in one article or one video, so you'll have to be tenacious and chase down whatever piques your curiosity. But I'll still try to get you started down the path of answering some of your questions.

The capacitors supplement the power supply by handling sudden, short changes in the load. The tests sweep through a range of frequencies one at a time. It's a powerful technique, but it has some limitations. For example, you have to know that the measurements will change if you change the DC voltage.

Determining if a physical system will work under all conditions and tolerances requires a model and some analysis techniques.