... when caught how does it realise it's landed and stop struggling to fly and allow shut down with left stick down?
When it's descending, it's watching the barometric altimeter for changes that tell it it's still descending. When the altimeter has stopped changing for a couple of seconds (despite the fact that it's continuing to reduce motor speed and keep the system level) it realizes it can't descend any further and will allow you to stop the motors.
As stated above, if you in GPS mode and you are moving, it will think it's being blown by wind and will try to compensate and fly back to where it was.
You may have better luck switching to ATTI mode after you get a hand on the landing gear.
As for hand launching... ??? I've never tried. I would try launching from a flat surface and kick the throttle up fast.
I've seen videos where an assistant hand launches. The pilot throttles up and the assistant lets go when they feel it pulling upward.
As above though, you may want to launch in atti mode to prevent it from trying to hold position.