The attic wiring should be protected and secured to ceiling joists or other wood structural supports.
Cable drop through attic multistories.
Then retract the fish tape to pull the cable through.
When cutting through drywall from the interior of a room use a utility knife and cut carefully you don t want to drill through a hidden wire or the paper.
I ve never run much coax but if are a 3 4 in hole might be a better.
Yes this should be corrected and it would be good to have the wiring and all the circuit connections inspected as well.
Make sure the tape is smooth so the cable can slide through the opening.
Use a piece of string that you can add a small weight to such as a steel nut or whatever you can find.
Drop the string and catch it in the wall cutout and use that to pull the cable through.
And use semi rigid wiring fish tape to pull your wiring down to your outlet location.
Carefully extend the fish tape from one opening to the other.
If you will need to fish wiring through a wall drill a hole through the wood plate in the attic only.
Pull the cable through with a fish tape.
3 8 is really only useful for a single cable run and i can t imagine running cable through a 1 4 hole.
This video shows how to install an attic fan to help keep your home cooler.