TVöD only decides the monthly enumeration of pay, and does not dictate what the employer can put as a condition in the contract. The money a PhD student gets is for their work done as given by the supervisor. This does not need be PhD relevant (if you have a bad advisor). You are supposed to work on your PhD outside these hours. That is why the restrictions (my guess). My answer does not cover what happens if no explicit restriction exists in the contract. I am inclined to believe it is possible (and not possible if you are a foreigner).

It is (almost) the same number in Germany, but in euros ;)

It is the same: you are conferred "facultas docendi". Since last 2 decades it is not the only route to Professorship in Germany.

Habilitation is simply a certified licence to teach. So, no. But semi-leading a group can count as experience.

Can happen if you know the reviewers are your friends and will back your decision without any consequences for you.