Wiring – Should I run cable through pipe

You've got a lot of different questions, so I'll try to answer the ones I can:

1. Coax sucks because of the necessary bend. You're better off going with a backless box like the one you linked to, because it makes running cables so much easier. (if you have a second person, have them push the cables up from below (or a straightened coat hanger or other wire to act as a needle, if the bundle of cables is too floppy), and then snag it from the hole with a wire bent into a hook) ... which you can't do as easily if you mount a box with little punchouts. Also, you then don't have to worry about crowding the box, etc.

2. It's easier to run lots of cables at once. What what you're planning already, I'd likely run an extra cat5e/cat6 cable, and then get an HDMI-over-twisted-pair (aka HDMI-over-cat5) extender if you wanted to go that route, or re-terminate it for RJ11 if you wanted to change it over to phone.

3. I don't know of any other way to get cables/pipes through the sill other than drilling, and it's allowed for plumbing, electrical, etc, so long as you then spray foam the holes afterwards (at least, it's required in my area, might not be in yours).

4. You only need to line up well enough to get it in the same bay, so you have a ~14.5" target. I cut the hole for the box first, then check to verify the location of the studs (I don't use hardware that requires me to attach to a stud, so I just have to make sure to miss it when cutting my hole), then measure off of some reference point that I'll be able to find down below. (electrical runs, walls, etc.) If nothing else, you can use plumbing or electrical for identifying where the walls are from below.

5. To avoid humidity issues, use spray foam to seal around the cables. (see #3). It may even be required by code in your area.

There's a number of things you could do, this is one I would do in your situation. These fans are made to fit inside sheet metal ducts. Go ahead and get 2 lengths of this stuff. You will end up with a joint somewhere in the room, but then the duct can run fully through both walls and there's enough slop in the fit that precise cutting is not needed.

Because of the joint, you will need a hanger support that anchors into the ceiling, which I assume is concrete. You would need a hammer drill to make the hole necessary to insert an anchor stud to which the hanger can be attached.

This is not the most attractive thing in the world, but it can be painted so that it's not too objectionable. Painting exposed ductwork is done intentionally sometimes as a desirable (to some) "look". You could also construct a soffit box to contain the duct, you end up with a sort of stair step on the ceiling. Given the extra work for this, it's easier to like the painted duct look.

To fill in the holes, get some cement backer board and cut to the size of each opening. Also cut holes to fit the duct or fan. For the size involved, the boards can just be glued in place with construction adhesive. You can also glue in some backup cleats behind the boards to increase the glued surface area if you like. The boards should be recessed about 15mm from the wall surface. The remaining space is filled with portland cement plaster in 2 or 3 coats. It is an obvious patch, but it sort of matches the wall and would be hardly noticeable if the walls are to be painted.