2" minimum separation between ordinary electrical wiring, and communication cables. At least that is code here in the US.
6-8 inch separation is usually preferred for long, parallel runs.
From your photos, you shouldn't have any trouble.
You can run the cables from the top of the stud bay/cavity to the bottom of the same cavity/stud bay and secure the low voltage box at the height you want your rack.
Tip: Once you get below the low voltage bracket use loosely attached zip ties the rest of the way down in the stud bay , this way you can pull the cables up and out of the wall easily after it’s sheetrocked.
Seems simple enough, thank you!
Welcome. Here is a more detailed answer
Hammer hook nails into the stud (make sure to hammer a hook nail within 4 inches of your main hole at the top of the stud bay, and hammer another hook nail within 4 inches of your low voltage box, and then hammer another hook nail within 4 inches of the bottom. Then run zip ties through the hook nails to secure your wires. Any zip ties below the low voltage box will be zipped loosely around the wires through the hook nail so you can pull the wires up and out when you are ready to terminate.
Basically just follow what the electricians do, but leave your stuff loose enough to pull back up and out the wall after drywall.
If you zip tie too tight you will have to yank hard to get one wire free then the rest will move easily, or you will need to cut Sheetrock to get your wires back out the wall.
Do conduits not exist where you live?
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