I'm a Tokyo ALT for Interac so I can answer all your questions!
The NT system you're talking is just the contract details, which is where you do everything solo and the other teacher just watches you since they can't interact.

All planning is 100% on you since you're not allowed to talk to them about anything classroom-related. It's due to law. Almost every single contract is for this and it's what I do!
The other system is Hakken which is pretty rare and I've never experienced it, it's team-teaching which I think is the same as JET.

I have a friend in Tachikawa and he's Hakken, but that's the only BOE that I know which uses it.
If you want to teach in Tokyo branch you should expect a NT situation!
Pay is the exact same regardless of contract, 23man/month+transportation. It's possible to get pay raises if you recontract but they're not very high.

Older teachers get a bonus for finishing the year but new contracts don't offer this anymore.

The only way to get a higher base pay is to be a head teacher for the area. I've heard that a couple of BOEs pay more but I think that's really rare. I think that Shinjuku is higher but that may have changed.
If you want to teach for Tokyo branch, I can give you a referral and you'd be guaranteed to get in. We'd also both get some extra money, which is always nice!
