Thanks for the advice, but going against the traffic flow means you will live inside Tokyo, as most traffic coming from outwards to the inner yamanote line. I bet it'll be quite expensive. My workplace will be at shibuya station.
Unfortunately 0% chance (getting a job offer is not that hard, but getting the visa is). Minimum req for an engineer visa is a degree or 10 years of exp.
There is a loop hole for non degree holder, but it's sketchy even for someone who had been working there before like me.

Of course there is another type of visa, but google will probably be more help.