Can I remove a 360 account but still Use it on an Xbox one without having the 360?

You might also want to goto the xbox 360 account protection page, and select require profile download, then follow steps on there to continue. This will remove the Xbox 360 as a trusted device, as it will need to log in using your password instead of automatically
logging in.
https://account.xbox.com/en-GB/profile/protection

Hi! unfortunately the only thing you can do is change account password. It's not possible to remotely remove accounts.

You should change your Microsoft account password because it is connected to everything. So you can do it from PC

Yes, you can. The Xbox One emulates an Xbox 360, so it will pull down your 360 profile fresh. What I would recommend doing is two things, account wise, since you didn't remove it from your last console. It's safe, so that's good. It happens.

First you'll want to add two-factor authentication (2FA). That will simply further secure your account, since
you don't know where it's going to end up. It would require that a 360 use an
"App Password" to log into your account, since it doen't natively support 2FA, but that is only making it more secure.

The second thing to do is log into your
Microsoft Account page, and click "More" > "Devices". From there you can remove your Xbox 360 from your account, effectively removing authorization for your account to log on to that 360 that you sold, again, simply further securing your account.

Other than that, you should have no problem playing your Backwards Compatible games on your Xbox One.

Let us know if you have any questions!

Just head to account.microsoft.com. There you could change the security options for your account.