Cat6 for telephone - Yes, but it's massively OTT for the application. Even simple Cat5e is massively over-spec'ed, but at least it's thinner, easier to route, and cheaper with no trade-off in telephony performance.
Cat6 to a HDMI socket - Maybe. It depends what you're expecting to do with it at either end of the cable run. Not that it's really practicable, but you wouldn't just wire up a couple of HDMI sockets with Cat6. For a start, there are 19 pin connections in HDMI. That would require running 3 x Cat6 for 1-to-1 pin connections. Second, there's a good chance there would be timing errors because of the different conductor lengths.
We use Cat cable as a way to link between HDMI-to-Cat / Cat-to-HDMI convertor boxes called
Baluns. Depending on cost and quality, cheaper baluns use some fairly aggressive compression tech which does impact picture quality. All else being equal, sending more gets a better result. At the top of the tree are baluns using a technology called HDBaseT.
running a video distribution network via HDMI cables or balun convertors made sense when the business of playing media was restricted to a central media player such as a Kaleidoscape because online streaming didn't really exist, and even if it did, the TVs of the day were dumb and "thin-client" media players were flaky. Things have changed a lot. Lots of media is now available online. TVs can decode and display the media files. Media player devices are available from a few tens of Pounds that eclipse the performance of older players from 6-7 years ago. There are still advantages in picture and sound quality terms for physical media such as Blu-ray disc and UHD BD. Also, streamed content isn't always available, or not in the Special Edition versions of physical media. For these reasons then, there's a good case to make for having a main media player in the family room for group viewing, But I wouldn't bother distributing that to the master bedroom or the kids rooms.
There's perhaps more of a case to be made for sharing say a Sky Q mini player at 1080p via the house RF cable system, or maybe being able to access the CCTV user menus, but anything else seems a bit redundant.
It isn't recommended to power anything from the lighting 'ring' that isn't lighting or directly lighting-related. The risk is that someone other than you might be working on it thinking it's isolated because it's not a light and then find out rather unpleasantly that it isn't.
Multiroom audio for the DIY'er normally means a wireless system based on Wi-Fi e.g. Sonos / Yamaha Musiccast / Denon Heos / Bluesound etc. (
link here to some of the usual suspects) or on progressively lower budgets a bunch of smart speakers from the likes of Apple or Google. A lot of this gear also has Ethernet sockets. A bit of wire just works and it keeps working regardless of what's happening with the Wi-Fi in the house.
The advantages with in-ceiling speakers are that they look cool and can give a better stereo effect than an single point stereo speaker. The performance gap between in-ceilings and decent smart speakers is closing. A couple of Sonos 5s will set the owner back £1000 for the pair, but they won't be far off the pace of a decent pair of £300/pr 6.5" in-ceiling speakers (+ fire hoods) [
Blucube BCK65 spkrs, Hoodie fire hoods] + the £600 Sonos amp. The bigger bass-drivers in the in-ceilings gives them a bass extension edge, but all other factors weighed in it's a closer call.
Of course, the in-ceiling speakers don't have to be driven by a dedicated streaming amp. They could just as easily be powered from the Zone 2 speaker outputs of an existing AV receiver or Speakers B out of a stereo amp. This changes the costings significantly, particularly if the amp includes streaming and NAS access already. .
The music sources are:
#1 free or subscription streaming - Spotify, Tidal, Qubuz, Apple Music, etc (Google is your friend)
#2 music trapped on a 'phone and shared to one of the speakers/streamers/multiroom components via Bluetooth and then distributed via the network
#3 ripped music stored on a NAS drive
Low-rent users will cast Youtube (complete with adverts) to their home network speakers
