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.
Cable drop through attic multistories.
Yes this should be corrected and it would be good to have the wiring and all the circuit connections inspected as well.
I ve never run much coax but if are a 3 4 in hole might be a better.
Carefully extend the fish tape from one opening to the other.
Pull the cable through with a fish tape.
And use semi rigid wiring fish tape to pull your wiring down to your outlet location.
This video shows how to install an attic fan to help keep your home cooler.
The attic wiring should be protected and secured to ceiling joists or other wood structural supports.
3 8 is really only useful for a single cable run and i can t imagine running cable through a 1 4 hole.
Make sure the tape is smooth so the cable can slide through the opening.
If drilling downward through the floor repeat the above procedure but expect to pass through 3 4 inch 1 9 cm sub floor and up to an additional 3 4 inch 1 9 cm of finish floor hardwood etc once 2 inches 5 1 cm have been penetrated it should be much easier to drill.
Then retract the fish tape to pull the cable through.
If you will need to fish wiring through a wall drill a hole through the wood plate in the attic only.
Drop the string and catch it in the wall cutout and use that to pull the cable through.