Pickups are usually the same distance from the string whether back or front. Too close and the magnetic field can actually pull the string so much it can ruin your intonation. there is a specific video in the Fodera set on pickup height.
You might need a bigger screw driver to move the screws. I've had that problem too and it took a bigger driver to do the job.
You might have to move the strings to set the neck relief. There are always suppliers of allen keys of all sorts on ebay or diy stores or motor stores.
Lefty loosey and righty tighty are when you look at the opening to the trus rod. On your Cort stand at the head end and look down the neck. Left turn loosens the neck, right turn tightens it.