The terminal should be a minimum of 2.3m horizontally from any structure to prevent turbulent air effecting the draft of the chimney so not compliant. No product can overcome this requirement.
As Woody suggests there may be some restrictions for converting the garage into a habitable space. These restrictions can also be private covenants attached to the deeds and nothing to do with planning permission. Sometimes it's just a matter of paying a fee to the company that built the house...
This would be adequate and easier to terminate. https://www.cef.co.uk/catalogue/products/2015279-0-5mm-5-core-yy-control-flexible-cable-cut-length-sold-by-the-mtr
Yes the OP could indeed if he/she chose to ignore whoever has done the calcs and drawings. Line 1 of Table 10 of Doc A. https://www.planningportal.co.uk/info/200135/approved_documents/62/part_a_-_structure.
Edge sheer? This could only ever be an issue if the compressive strength of the...
For RGBW LED installs I always use this. https://www.pfjones.co.uk/thin-wall-5-core-auto-cable-30m-100m-tw05-01.html. They do a 4 core, TW04, that's great for RGB LEDs too.