Also, starting next year, I'll be going to a trade school for auto mechanics, so would that be a viable career as well?
You mean in Japan? The land of Toyota, Nissan, Mitsubishi, and Honda?
A lot of people talk about going to Japan to do jobs that normal Japanese people do (manga artist, j-pop singer, convenience store worker, etc.), which I guess is possible, but... I just have the feeling it would be hard. Taking cars for example, when the employer has to choose between a foreigner (who needs a visa, will most likely be taking money out of the Japanese economy, and doesn't speak Japanese as a first language) and a Japanese worker (who... is Japanese, [speaks Japanese, will keep money in the economy] and has probably trained from a fairly young age at an actual Toyote/Honda/Nissan school), I can't think of many situations in which he'd choose the foreigner.
Yes, it is possible
to get jobs like this... But I think you'd have to be in the right place at the right time and catch a shortage of labor so they'd have to hire you. It's a million times easier to get a job that normal Japanese people can't do, like teaching English or some job where you have to work with other foreigners a lot.
As for a place to live, if you were planning on working soon after you arrived, and moved into a fairly rural place, 20k would be sufficient. I live off less per year, but I'm in a teeny apartment, no car, and I don't have to commute anywhere (trains get expensive!!).