Hi zaibakk
I don't often post here but I have opinions on Psionics and Blaster Launchers too so I thought I'd share.
1) I also think that not being able to use PSI-amps at all would be too much, also it wouldn't make much sense if you could sell them but not use them (who would buy them if they had no use?). I also agree that Psionics are too strong in the base game, I've made some changes of my own to try and balance them if you're interested:
2. I play the (mostly) vanilla game + my own tweaks, and I find I rarely use the Mind Probe anyway. Only in the late game to see which alien is a leader or commander really, or sometimes I'll bring one along to check how badly injured an alien is if the soldier holding it has nothing better to do. In OpenXComExtended you could set the Mind Probe (or any other item) to require psionic training, but it doesn't mean it increases your psionic skill to use it, if it did it would be cool and would be a change worth making IMO.
3. One issue is that non-psionic aliens currently use the blaster launcher against you, so should the restriction apply to them too? If so, non-psi aliens should probably be given different weapons other than one they can't use. If not it wouldn't really make sense that you get a restriction that the aliens don't get (it's important to me that everything have a background story that makes sense!).
In my own mod I've completely disabled the blaster launcher for human use, it's just too good as it is, you can still research it to go own to the other requirements though including the Hoverank/Launcher which brings me on to:
4. I don't actually think the Hoverank/Launcher needs to made any weaker (in vanilla anyway don't know how it works in FMP) for the following reasons:
It already takes up 4 spaces but only gets to fire one missile that's weaker than a blaster bomb, so soldiers with blaster bombs are already better. Plus it's very expensive to make and it's ammo is very expensive to make, so it needs to be good to justify the cost. I always like to think the Hoverank/Launcher has some clever programming that's updated with a map of the battlefield and can calculate and communicate wirelessly with the missile where to go, and that's why it doesn't need psionics even if the blaster launcher did or in my case is just unusable by soldiers.