They need to be in some kind of enclosure
https://www.toolstation.com/ip20-choc-box/p86064
https://www.toolstation.com/wagobox-221-4-junction-box/p54159
If it's a new circuit then notifiable. If you could find suitable locations and spur (or extend the ring) from an existing circuit then no need to notify.
You could use SWA but if you could find a cable run from the inside directly into the outdoor socket it would look much neater.
With your...
If the OP is correct and the cable is connected in via a 32A MCB, then surely negligent of the installer not to have tested properly?
If the OP took some pictures that could help.
What make are the storage heaters? Can you see a model number?
(about once every 2 or 3 years one of mine stops working, I isolate, take cover off, hoover out the accumulated dust and click the thermal reset button. Takes 5 mins)
Put rubber in body, wider steel ring with flange to rubber, other steel ring with flange to outside (to trap wire shroud), brash washer, nut.
See how that looks
I assumed this was commonplace? Are we really saying that to swap an electric shower requires visits by two tradesmen? As a competant DIYer I'd happily do that in my own home. What about boilers? I assumed you did the power to the FCU and then plumber wires up boiler and stat etc...
The DP switch must be faulty. What make is it? Did you buy it specifically, or is it old stock?
I'd be changing that/returning that.
Is the MCB new? What make?
I was thinking a **** heater was a very niche product I had not heard of. Given the intimate nature I assume would require 30ma RCD protection and a suitable IP rating......
I used the Wera set I have today and had forgotten how easy these are to use. Was thicker material so did pre-drill but makes it so much easier than using separate tools.
https://www.aircondirect.co.uk/p/865335/1000-btu-panasonic-powered-easy-fit-inverter-wall-split-air-conditioner-with-5-meters-pipe-kit-and-5-years-warranty
I've seen many for sale
What you are trying to achieve is available off the shelf for a little over £100. My advice is buy the kit and get out in the workshop and make something......
https://toughleads.co.uk/products/stand-alone-automatic-dust-extractor-switch-110v-16a?variant=33606828490840