Are positron rifles available to Yamatai weapons developers?
What do you mean (Explain what you mean by "available" and "Yamatai weapons developers")? The answer is probably yes, as anti-matter is not a restricted technology/weapon under YSE law.
How small can a positron weapon be when Yamatai technology is involved?
Some positron rifles for power armor exist.
Do you think a power armor would be awesome with a back attachment that has tenticles?
Maybe.
How the hell does the Demon armor hold so much 35mm ammunition for it's chaingun?
It carries a large backpack magazine.
What sets the Mindy soft core insert apart from the Kylie's soft core insert, and what are the technical reasons for the two different types?
The original requesting party for the Kylie M3's design disliked the flesh and wanted a synthetic instead. The synthetic insert's main difference it that it doesn't recycle things as well and cannot regrow itself after damage.