Thermostatic shower

I would get a plumber to do it for you

You can purchase a “shower fixing kit” around £15... basically plates that fit to the wall and have an olive and nut to tighten to 15mm copper hot & cold feeds coming through the plasterboard..the shower then fits to this kit...i wouldn’t recommend speedfit..

Something like this would do the trick. You would need to tape the thread with PTFE around 10 times around the tread before screwing it in. You may also be able to buy these in a elbow design. If you need the bend you can add a spigot elbow onto it. https://www.toolstation.com/brass-male-adaptor/p13195 You can also use compression joins directly on plastic pipes just remember to add inserts.

Not entirely sure I understand the question, but going to guess that you are trying to connect a thermostatic exposed bar mixer shower valve. If this is the case, you need to consider that you are not just trying to connect the hot and cold, but also support the valve itself. To this end, there are a number of different products out there to do this. Screwfix usually stock a couple of options, but you might get more helpful service from a plumbers merchant. Once you have the right kit, the rest should be pretty obvious. Worth pointing out that how you make a sturdy and long lasting connection to your substrate (plasterboard) is probs out your biggest challenge here... it may be sensible to place something else in the mix (some timber or plywood) to enable simple and resilient fixings for the wall brackets...