It's sort of hard because in your rant, you've been asking so many different ridiculous questions. Have you now given up on asking my opinion on your fantasy stories?
But if you need an answer, it's at whatever age the child, parent, and doctor decide as appropriate for that case. I have no problem admitting that I haven't spent my life investigating the use of puberty blockers so I'll defer to the actual experts.
And yes, if for some reason a teen wants to start puberty blockers (after puberty has started?) and the doctor thinks they are capable of making informed decisions, the parents don't need to get a say.