They used to be much more expensive, but now, $30 is a pretty small cost for the time you would save.
Drill through the wall with a flex bit starting in the place that you want the cable to terminate. Go slow through the bottom wall plate, and once you feel it go through, stop. If you have no fish tape or rods, stick a straightened coat hanger through the hole and find the other side of it under the house. Tape your wire to it, and pull it back through. Repeat the process as many times as you need to until the entire job is done.
Definitely drill and mill, the threading would be too large to be a tapping bit - it's one of these - https://www.amazon.com/Agile-Shop-3-8mm-Titanium-Cutting-Carpenter/dp/B01FIERWO4/ref=sr_1_6?dchild=1&keywords=drill+saw&qid=1616955759&sr=8-6
drains clog...if you have long hair in the family it might be worse than others
yes, get a snake. it'll save you time and money as a home owner!
https://www.amazon.com/Cobra-86250-Deluxe-Drum-Auger/dp/B006LWC6QM
then get a drain screen that fits your shower
https://www.amazon.com/Catcher-Strainer-Stainless-Bathroom-Different/dp/B081H55QLM
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An auger bit file may be suitable as there is a smooth edge Lie-Nielsen or Amazon
IS the drywall/plastic the side where the TV is mounted? Kind of hard to get a perspective from how the picture is.
If so that cross 2 x 4 makes sense, builders will install bracing to help reinforce TV mounting, to make installing wall mounts easier.
If you want to reach it and drill through it, you need to get a long flexible drill bit like this https://www.amazon.com/Irwin-Tools-1890759-Installer-54-Inch/dp/B00LLGT4GI that'll help get you the angle and distance you need to drill through it, its also great for pulling wire through those drilled holes as well.
A power drill can be a wonderfully versatile tool, depending on what bits & attachments you have. Specialized tools are of course better if you can get them, but if you have limited space and a limited budget a power drill and the right bit can often get the job done.
I've used saw bits like these for rough machining/shaping of woods, resins and clays.
Flex bit for drilling down through subfloor. Take it slow and easy. Hit a snag, stop and back out and move over a bit. Knots in the wood will destroy these things. Use razor blade and/or drywall knife to knock out wall plate size hole. Plenty big enough to put flexbit through. Used this many many times running AV cabling
Irwin Tools 1890759 Flex Shank Installer Drill Bit with Auger Tip, 3/4-Inch Shank, 54-Inch Length https://www.amazon.com/dp/B00LLGT4GI/ref=cm_sw_r_cp_apa_dp8CAbDY3MD5J
Yeah those are metal bits. There are a number of kinds of wood bits. Like: https://www.amazon.ca/Irwin-Industrial-3041006-Speebor-6-Piece/dp/B000LQ905E/ref=sr_1_9?ie=UTF8&qid=1511098255&sr=8-9&keywords=wood+drill+bits
or for larger holes this type is better: https://www.amazon.ca/8milelake-Forstner-Individual-Woodworking-15mm-35mm/dp/B074N4819N/ref=sr_1_28?ie=UTF8&qid=1511098331&sr=8-28&keywords=wood+drill+bits
>Should I call an electrician to install an ethernet port?
Why not do it yourself and save hundreds of dollars?
Is there a basement or attic? Use that for horizontal runs.
For the walls, if you have a typical twigs and plywood house, getting between floors will be a bit tricky, but not super hard. Cut a small hole at the floor and ceiling along the wall in the 1st floor, using a long, flexible drill bit drill down into the basement from the hole near the floor. Drill up to the second floor the same way. Try to keep the bit centered on the sole plate/top plate.
If you have to use the attic to run from one side of the house to the other, you'll need to repeat the above process on the second floor to get to the attic, then once you're in the attic above the bedroom, drill up from a hole near the ceiling to get into the attic from the bedroom, then cut a hole where you want your wall plate.
Then you'll have a few small holes to patch and paint.
Take my well meaning reply. No you don't. :) They don't work well with twist bits. The are designed for auger type bits. Like this; https://www.amazon.com/Irwin-Tools-43616-1-Inch-Braced/dp/B000CD1MPW/ref=sr_1_7?ie=UTF8&qid=1492027142&sr=8-7&keywords=hand+drill+auger+bit Try one like this; https://www.amazon.com/Schroeder-Hand-Drill-4-Inch-Capacity/dp/B000JRDLVY/ref=sr_1_5?ie=UTF8&qid=1492026929&sr=8-5&keywords=hand+drill
Buy one of these: https://www.amazon.com/Greenlee-09-03-54B-DVersiBIT-Combination-54-Inch/dp/B000FCGT12
You can stick this drill bit through the cutout for a wall plate, drill through the bottom wall plate & subfloor, then go to the basement & tie your cable to the drill bit and pull it back up through the floor.
I think what /u/saintnicster was getting at more than anything was to not use a hole saw to go through studs (at least for wiring, plumbing is a whole different issue)
Edit: I also hate spade bits. These have done wonders for me but are starting to get dull after 4 years
Expansion bits are for when you need a non standard size.
Irwin Tools 43616 1-Inch Hand Braced Solid Centre Auger Bit https://www.amazon.com/dp/B000CD1MPW/ref=cm_sw_r_awd_UP23vbS858N45
Not as good as the older ones made in USA, but they are still made and do the job.
>I don't even know how to do it
Oh, man, you need a Flexible drill bit.
With a 54" bit, this lets you drill through 3 studs (16" on center) from a single hole in the drywall. You've got to cut a hole every 5 feet or so, but if the hole in the drywall is cut properly, you can just install outlets if you don't want to patch it.