Yes! Go to sign in on the dashboard and then choose " Recover Gamer Tag " then enter your gamer tag, email address, and then your password.
Yes, they both utilize your Microsoft account, therefor you can have the account on both your Xbox 360 and your Xbox One. You will just have to bare with being prompted with "This account was logged in on another console" each time you switch from the 360 to the One.
Yes, your account should transfer.
save
Yes, simply connect the memory unit to the new Xbox and sign in with the account.
yes they would have to log in to your account and license transfer it to there xbox.
No.
You cant, the only thing you can do is transfer the memory to the new xbox 360 slim with a transfer cable.
no you cant sorry
You cannot transfer messages onto a flash drive because they are saved onto your account and not your 360.
yes you'll need an xbox 360 an xbox 360 transfer cable and a mac or PC
when you take in your old xbox, they let you keep your hard drive, which has your account and membership
No I don't think you can. I'm sure that you need to buy a transfer kit. I'm not sure where you can get them from.