Permanent ban while having a normal suspension

You would need to go to http://enforcement.xbox.com for information about the ban and to see about submitting a case review.

There's no set number of suspensions that can lead to a permanent ban. You can receive a permanent ban without ever having received a suspension before.

There's no set number of suspensions that will lead to a permanent ban. You can get a permanent ban without having any prior suspensions. Or you can get 5 suspensions and then get a permanent ban.

They recently updated/moved the enforcement site and I think it's had some issues. It doesn't necessarily mean your enforcement history is clean.

That would be entirely up to the enforcement team. There's no set number of suspensions you can receive before getting a permanent ban. You can get a permanent ban without have any prior suspensions.

If it's a temporary suspension, you'll have to wait until the suspension is over. If it's a permanent ban, then that won't be possible. There is no way to sign into a banned account.