A reasonable cost of living estimate is USD$2000/mo to cover rent, food, basic living necessities. That figure can (and probably will) go up wildly depending on where you want to live and how much extra you will spend on entertainment, etc.
You can find car parts nearly everywhere in Japan, except maybe rural villages and the more remote islands. If you're looking for factories, they're all over so you'd have to ask for a specific company or design firm.
If you have near-fluent Japanese, you could probably find a job here working in import/exports. There's relatively high demand for exporting Japanese car parts abroad, and a person capable of Japanese/English is relatively invaluable in car parts exporting. But I would suggest getting a job at home with car part importing (from Japan) in order to build up contacts (import/export is all about knowing the right people). Coming to Japan without knowing a single person is pretty much useless.
And speaking in general, there's nothing too special about Japanese car/engine factories (except maybe the hermetically sealed chamber in the Nissan GT-R engine production). It's pretty much the same as anywhere else, really: they refine metals to remove impurities; cast them in molds to make the base engine block; then use heavy machinery to assemble the main block, and then complete the rest by hand. You could probably find a video of that on YouTube -- save you $20k and a time-consuming trip to Japan.
If you're interested in "what makes Japanese engines so good" you probably need to look into engine design, which means engineering/design firms, which are managed by the big manufactures and hidden behind many layers of NDAs and lawyers -- once again, all about having the right contacts. As a layperson, the absolute best you'll be able to do otherwise is to see the dumbed down made-for-children illustration of how an engine works at some car museum.
Also, Europe makes good engines too, and many that are better than Japanese engines in the same class. Plus there's the whole difference between petrol, diesel, biofuel, fuel cell, and now hydrogen cell engines (though technically fuel cell and hydrogen cell engines are both just electric motors), and some companies are better at certain engines than others.
Points in general: your standard tourist visa into Japan is good for only 90 days and does not permit work. You can apply for a work visa but will need to get that sorted out before you come to Japan and will require someone inside Japan to sponsor you.
