Hi!
About 2, 3, and 4, I have no idea, actually. Do you know if Praat has functionality for it, and how to access it? Parselmouth is in the first place a Python interface to Praat, so will contain all the functionality from Praat. If you know how to do it in Praat or have an existing Praat script you want to integrate into Python, I'd be happy to help you. But I don't know these measures, myself, so I would first suggest to investigate how you can get these measurements in Praat.
Kind regards
Yannick