Electrical – add an outlet for electronics to a lighting circuit

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:

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.

Your interior speakers are the easiest. Unless you already have cabinets, ceiling mounted speakers will provide good ambiance while being the least visually obtrusive; you can get ceiling mounted speakers with equivalent power and frequency response to a set of cabinets. If you choose to do wall mounts or cabinets, you'll need fish tape or a fish rod in order to run the wire through the wall. Here is a fairly decent video explaining how to fish wire through a wall. I recommend you install a wall plate with a terminal where you can connect your speakers. If you're a true audiophile, there is no substitute for a properly aimed set of high quality cabinets.

For the exterior speakers, ceiling mounts are (obviously) not an option. Fishing through an exterior wall is complicated by insulation as well as code requirements regarding weather proofing. You'd follow essentially the same process for an exterior wall as for an interior wall, but your holes need to be smaller and sealed. Fishing wire through fiberglass insulation is a bear, so be patient. There are gaskets and grommets that you can use along with silicone caulk to seal the hole on the exterior wall. Since you won't have any flexibility for pulling extra wire through once you've sealed the hole, I recommend mounting a terminal inside a weather proof low voltage junction box. You can then run any length of speaker wire from there to wherever you mount your speakers. If you mount the junction box high on the wall, it will make fishing your wire through an insulated wall easier, but reconnecting speakers more difficult.

In both cases, you can and should run your wire through the attic. To avoid interference from electrical wires, make sure that your speaker wire never runs parallel to an electrical cable. There are also cable organizers (raceways) for running your wires that shield your speaker wires from interference and keep your attic from looking like a mess.