It really depends upon how old and how big the trees are. Could you post pictures, please.
When to prune also depends upon where you live. Could you please complete your profile with your location so that we have an idea of your climate? Just a zone won't help - we need to know your city/state/country/continent.
In some places you could still prune, without worry that the trees will put on a lot of new growth that would then be subject to frost damage. But other places are already getting frost and even snow (picture from Lk. Tahoe a couple of days ago).
As far as using netting, you have to put the netting on after the flowers have set fruit and the fruit is sizing up. Otherwise the flowers will poke through the netting and form cherries outside the netting which will of course defeat the purpose.
Please be very careful of using bird netting. A lot of other critters get tangled up in it and die. I tried netting my lychee tree a few years ago, and not only did it not stop the birds or the squirrels, it had dead bodies entangled in it every day until I removed it. Mice, squirrels, rats, birds, snakes (which are very beneficial here at controlling rodent populations). You name it, I killed it in just over a week! Very sad and upsetting.
Now I use a motion-detector sprinkler to scare off the critters both night and day, and it works great! Look for a "scarecrow sprinkler" on Amazon.
