If your wall is closed up then you don't have to worry about it. It looks like class 2 wire is rated to go into walls. Only use wire that is rated to be in the walls for uses like what you have. The only things to worry about with class 2 or class 3 wiring is:
- Class 2/3 should never be used in the same electrical box (without a low voltage divider or in the same conduit with your house wiring.
- Class 2/3 should be kept at least 10" away from house wiring. Try to run in a separate bay.
- Remember when crossing house wiring with class 2/3 it should be at 90 degrees.
If your wall is open then if you can spare the money for ENT or smurf tube (bendable, corrugated, PVC that is usually blue) then that will give your wiring more protection. It is sold in 10ft lengths or 100ft coils. You can run low-voltage class 2/3 or regular house wiring, but not at the same time. It will also give the transmission that is carried on the class 2/3 less interference when around house wiring.
![ENT - Electrical Non-Metallic Tubing](https://i.stack.imgur.com/dpiHR.jpg)
HDMI and speaker wire are basically signal wires, not power wires. Both the voltage and amperage is very low. Indoors it is safe to run these hidden or exposed without channel or conduit if they are properly rated. See this Q&A for a discussion of proper rating.
When channel or conduit is used, it is either for convenience in handling, and to keep the wires away from other materials, or it is used to improve the aesthetics - channel can be painted and looks neater than cables.
There are limits as to how much signal wire can be run in cable or conduit, but this is generally a function of pure physical space and ability to pull wire, rather than heat or safety. Speaker wire can be tacked to baseboards or other molding if that works. be careful to avoid breaking the insulation or the inner wires when stapling, and if you put wire under moldings, be careful not to nail through. Its not a danger issue, is a broken wire/no signal issue.
Power, including extensions to run a projector, is very different. No code allows extension cords to be buried in wall. I don't think any codes allow extensions to be tacked to baseboards. Also power cables should not run parallel to signal wires - they can cause interference even though many signal wires (like HDMI) are shielded.
You need to bring a regular, properly installed power line to the projector. This can be properly installed NM cable inside a wall to an outlet box. It can be surface wiring, but this requires standard metalic surface channels and boxes such as this and this:
![wiremoldbox](https://i.stack.imgur.com/oydYB.jpg)
One other note. Lampcord is often used as speaker wire. It is the same as is used for AC power cords and small extension cords. If you are using such wire, be careful, if you are burying in walls or stapling, that it is speaker wire rather than power carrying wire.
Best Answer
There are wall plates that are designed for your situation.
Power
For power, you can add the socket as you described.
Low voltage
For HDMI/signal/etc low voltage stuff, there are a number of options. Running conduit is the best for future flexibility.
I personally like just having a cable sticking out of the wall, rather than putting connectors behind the TV and requiring a bunch of short patch cables. There's "flexible opening wall plates" that have rubber grommets in them that work very well for this purpose. These work very well with a low-voltage junction box (which basically is a junction box with no back)
You can terminate the cables near your equipment the same way, or install actual wall plates, depending on your needs. I prefer wall plates with jacks (built-in or keystone) for that situation, because it's neater and allows you to easily disconnect stuff while cleaning/moving/whatever without a bunch of cables hanging out of the wall.
Combined
There are also a number of products that combine both power and low-voltage that work really well behind a TV.