Okay, I had a look at this today, using B1009.31.1 and the "4 F-35 vs 4 J-20" save (which BTW is a rather poor example for lofting, because at the distance the AMRAAMs are fired, there is no room to loft, so they effectively fly straight in).
For comparison, I also used another test scenario against non-VLO targets (Su-30MKI & A-50) where there was sufficient distance to exploit lofting.
1) There is an issue with excessive aircraft climb/dive rates, which can cause a target (such as the J-20 in this case) to very rapidly get out of the AMRAAM acquisition cone in the vertical plane. This has been fixed for the next update.
2) Re: AMRAAMs severing their datalink once they go autonomous. To our knowledge, this is the RL behavior. Even the AIM-120D (and Meteor AFAIK) with its two-way datalink does this. Our available information does not suggest any torpedo-like "offboard seeker" ability. If you have sources to the contrary that you can share, please do.
3) Re: LO targets having a good chance of evading seeker acquisition even if they are within the physical cone. Well yes, that's part of the appeal of LO/VLO.
4) I did not observe any pre-programmed "high diver" AMRAAM behavior. (I say "pre-programmed" because in one case, a lofting AMRAAM was re-directed to a tree-top level target which had just evaded another shot. The missile was originally cruising high for a more distant target, but because of the redirection it had to abruptly snap down in order to catch up with the new target in the weeds. This was the correct and desired behavior.) If you do notice any such behavior, please open a new thread specifically for this.
A general observation: You are shooting at highly agile (e.g. Su-34/35) or LO/VLO (J-20) aircraft, or both (e.g. F-22, Su-57). _Of course_ they'll pull out all the stops to ruin your shot. _Of course_ some of your shots will miss, or be physically outmanouvered (especially at long range). Plan for that.
The real criterion is: Do the same difficulties appear when engaging "easy" targets? I haven't observed this in repeated tests.