1/2) I've been impressed by the focus of K3iii in general - I cant speak specifically about the eye focus technology.
3) not having had the K3ii, I cant speak for the value of upgrading your crop body, IMO there is always an argument for better / different glass. The DFA 150-450 was a huge upgrade from my Sigma 120-400 OS HSM - a bit pricey, but the WR designation and DC motor are compelling features.
Considerations you've listed do not include the high FPS, quicker write speed or the deeper buffer. Switching from one the other, the K-1 is a Cadillac, but the K3iii is a Ferrari
Good luck!