Leg Training.

Do gymnasts do weighted pistols? And how do you progress to full GHR?

The fact that you're asking these questions tells me that you haven't read the BtGB book. None of the programming on these forums will be clear without reading it. Do yourself (and everyone else) a favor and buy the book, read it, then come back with questions afterwards.

With regard to your first question: yes, at a certain point in their progression they do weighted single leg squats.