Can be bad. A poor nut connection could be held together by the tape.

No actual electrician I know of uses tape, and in fact they use it as a tell if work has been done DIY or licensed a lot of the time.

Right now we just use bulk fiberglass to accomplish the exact same thing at a extremely small fraction of the cost for basically identical performance. It's a nonstarter.

Drill or punch a small pilot hole through the center of where you want the cable management hole. Then use tin snips to cut through the mat around the edges of where you want starting from the pilot hole. You can then pop in a grommet to make sure the edges aren't sharp. Just make sure to cut the right size hole for your grommet!

The product you are using is not really a wood finishing product. It's primarily a fungicide designed to, well, preserve wood - things like joists and floorboards. It doesn't repel water. I honestly would not use it for an interior project like a desk particularly if you're eating off of it.

You need to use a proper top finishing coat like a compatible oil based polyurethane. Sand down to 220 or so like the previous comment and use a few coats of poly sanding lightly with 320 or higher grit in between.

No, generally you set the floor to a few degrees higher than the desired room temperature and heat loss in the room means the ambient air temperature is a bit lower than the floor. Nice and comfy, and if they do shut off they go down to ambient and then turn back on.

The problem here is that the floor heating elements are being controlled via a temperature sensor on the wall, not embedded in the tile. It leads to big on/off temp swings at the floor.

You run the underfloor heating off an independent temperature sensor installed in thinset under the tile, not a temperature sensor attached to the wall that might even be in another room entirely.

This takes a bit of work to figure out what temperature setting in the floor corresponds to a comfortable room temperature (usually a few degrees higher than the room) but the floor will be pleasantly warm at all times and not have the big temperature swings you noticed. You also need a controller per room or zone.

The way your friends have it leads to weird on/off switching behaviour of the floor heating as you noticed. It should be controlled based on the floor temperature, not the room.

No, you need a properly insulated and plumbed house (no pipes in exterior walls or unconditioned spaces) to prevent freezing. A trickle of water is advice for warm climates that might occasionally see freezing temperatures, it's a coping mechanism for a poorly designed system.