Wiring – Do I need to “protect” low voltage cables that are run through an insulated wall

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.

The most important aspect of speaker wire is resistance. There is a ton of junk-science and stupid audiophile marketing claims that will try to confuse you and make you spend absurd amounts of money, but don't be fooled.

Wikipedia actually has a good write-up on it:

Resistance is by far the most important specification of speaker wire. Low-resistance speaker wire allows more of the amplifier's power to energize the loudspeaker's voice coil. The shorter the cable and the greater the conductor's cross-sectional area, the lower its resistance. Depending on the hearing ability of the listener, this resistance begins to have an audible effect when the resistance exceeds 5% of the speaker's impedance.

They also have a chart: for 35' at 8Ω, you're good with 18 or 16AWG.

All you need is basic stranded cable. Don't pay extra for fancy brands, or "oxygen-free" or "hand woven by the dalai lama" or whatever (unless you have the money to burn and really way to, I guess) as there's really no difference -- you can use lamp cord, if you want.

In proper tests, the best audiophiles can't tell the difference between $500/ft "top of the line" speaker wire and coat hangers -- and if you can, James Randi will give you $1 million (sorry, a bit OT from your question, but people that believe in this nonsense really piss me off).

For in-wall applications, you should get wire rated for in-walls - which basically boils down to fumes that the wire gives off in a fire. There's a good article on Understanding In-wall Speaker, Video and Audio Cable Ratings on Audioholics. In short, in a 1-2 family dwelling, any cable with the following ratings is suitable for in-wall: CM, CMP, CMR, CMG, CL2*, CL3*.