Bit like 5 axis cnc....Square nuts are better at resisting torque and easier to make a pocket for. Something I haven't tried yet but intend to use is to model the pocket inside a design, pause the print at the appropriate moment, insert the nut then resume the print over the top. Bit of a faff but I am still so new to the game, I often sit and watch the thing anyway. I find it quite relaxing...
Helicoil wire is usually 0.75 or 1.0mm section so lots of standard taps will work, but many do not, requiring weird tap sizes
Which bit of it is this or these dimensions? Surely the wire is diamond in cross-section, with two 60 degree and two 120 degree angles. Any picture showing dimensions? The calculation is not trivial as the major dia. of the inner thread will be opposite the minor dia. of the outer thread.