Check that the socket you run the spur from is on a ring circuit, eg with a 32A MCB/RCBO
That's OK
Because your media devices will not draw much current, I think the same single feed could be used for the 2kW fire as well, but maybe best on its own socket.
Sorry to sound blunt, but that sounds a little arrogant, unless that has already been discussed and agreed!
'Sign off' is a declaration by the electrician that he has designed the circuit to the regulations, that the workmanship is satisfactory (terminals done up to acceptable torque, wiring insulation meeting requirements, sleeving present, IP met, no damage etc etc.), then testing with calibrated instrument(s), and the results recorded on the Minor Works Certificate (or EICR/whatever).
As a result of that formal declaration the electrician often assumes some responsibility for safety, with associated legal implications for him/her.
A visual inspection and testing doesn't necessarily give all the necessary information, so quite understandably many electricians won't agree sign off other peoples work, and you might argue it's unethical.
As a minimum I suggest you discuss what you would like to do with the electrician you'd like to use, and let him decide if he's happy for you do the work. Sometimes a compromise can be reached with prep, running cables etc. and the electrician terminating the accessories.