Ok, here goes with some answers, I hope they help!
Very fine tuning:
As long as the pulley is positioned snugly up under your friction hitch, you can tug it and wiggle your hips to get those small adjustments. The friction of your rope around your tie in point can hinder fine adjustments if the rope is not sliding easily. I have been up trees with rough bark and trying to one hand the slack, because the friction around the tie in point is quite a lot, I could not pull the slack one handed (mind you I don't weigh much)
Jumping to higher branch:
Again, as long as the friction is not too much, yes you can pull in the slack one handed.
Foot Lock:
Yes you can foot lock with the pulley, you may not get as much distance on each pull as you are not actually pushing your friction hitch up as far as it can go. Be prepared for a bit of slack as you reposition your feet.
Detaching:
I use a bit of small line, a tiny accessory clip and a CMI pulley, It can be a bit twiddly to detach, bit maybe that's just due to my system! when decending I find I have to let the pulley down a bit to allow me to slack off the friction hitch to come down. It's a bit trial and error, and I'm still experimenting some.