Banger,
I can't answer all your questions, but I have some suggestions/comments.
If you are in a junior position an internal mentor could work (assuming your organisation supports this), but as you become more senior I feel that an external mentor could be better, because it would be useful to have someone who is impartial with whom you can discuss real life scenarios that you encounter.
I should also point out that one way or another mentors often get paid, either as part of their salary because mentoring is part of their job or they get extra payment because it requires an extra time commitment over and above their normal workload (my wife has done this, but not in
HR). Obviously an external professional mentor would have a fee structure.
You could get lucky and find a friend who has the necessary skills and experience to mentor you free of charge.
As for choosing a mentor, I guess it goes without saying that it needs to be someone who has relevant skills and experience and who is quite accomplished in their own right.
It's an interesting topic and I will be keen to hear what others have to say.