This is somewhat accurate but it is very indirectly related to the pipeline lenght. A longer pipeline requires more logic than a comparable shorter pipeline and, in this respect, a longer pipeline leads to higher power draw
Not necessarily, since the issue of activity factors come into play. Dynamic power draw (which is still the dominant factor for processors in the market today) has a linear correlation with signal activity. A long pipeline with low signal activity due to whatever reason (architectural or good design) will have lower power draw than a short pipeline that is switching constantly.
Another thing is that a fast-switching transistor should require thinner gate-oxide channels, which makes the dielectric's insulating ability diminish greatly, which leads to higher current leakage. The problem with Prescott was that it was huge (for a 90nm CPU) and it operated at high clock speeds that required fast-switching transistors.
Using low-Vt transistors is a design choice. By pipeline depth, netburst has fewer transistors per pipestage than other designs, so blowing up leakage power using low-Vt is a last ditch effort. Besides, leakage was the least of prescott's concerns imo.