Congratulation!
Some of your questions I can hlp with:
The heater should be a pull knob if its like me, it will operate a valve in the engine bay that diverts coolant via the heater. Mines a bit like an older choke cable.
Morgan sell cases and also the gear knobs (see their online shop). Others if course are available.
The handbrake is classic Morgan stuff and I'm not aware of any other options. Always park in gear as they're not called fly off for nothing

Cream dials can easily be sourced. Just google smiths instruments. You should be able to get direct replacements. Bet source of dash is from
here . Only ever heard good thinks about MK's work.
We like photos!
Above all enjoy your car.
R.