JET contracts are for a maximum of 5 years. Half of JET ALTs don't renew after their first year. It's not a career with JET.
Market here is flooded with teachers and wannabes. Be prepared for a lot of legwork to get that first job, and salaries are falling, and benefits are not being given out as freely as a few years ago. Are you coming here to look for work (more opportunities, but expensive to support yourself meanwhile) or looking while you are still there (cheaper, but far fewer opportunities, and you may still have to travel within the U.S. and pay your own expenses to the 1-3 day interviews)?
You have a lot to learn about that. Have you ever even visited the country? If not, I strongly suggest you come for a visit and try to immerse yourself a while. Tourists are not residents who work, so that will be hard, but keep your eyes open and network.
Trick question. Obviously, learning the language will help your way around, both as a tourist and as a potential employee. As well, your second point is true (experience is good, that is), and a boatload of people live here without learning much of the language, but why bother doing that? Just living and working here will afford you the "experience"; to grow to understand the culture, it all depends on how far you immerse yourself and keep your eyes open.
Shrill J-pop female singers? Yuk. Enka shriekers and wailers? Ugh. How can you learn to love a language from music? It doesn't follow grammar or pronunciation rules, and nobody speaks like they sing. You just like the music, I think. To each his own.
"A little patriarchal"? I thought you said you enjoyed (therefore understood) Japanese history! You're in for a very rude shock if you ever get here.