1. More than likely the swap will involve a VVTi engine from an Aristo (as Supra engines rarely come up for sale these days) Assuming the engine comes with all ancillaries like turbos, alternator, power steering pump & reservoir, aircon unit, ignitor etc. then off the top of my head you'll need to source the following as well as the engine;
Rear sump setup (budget £4-500 for this alone the way prices are going)
TT engine ECU (If it doesn't come with the engine)
Speedo dials from a TT car as the NA rev counter will not work properly with a TT engine (budget £2-300 for that)
VVTi Airbox or an aftermarket induction kit (£2-300)
TT Radiator (thicker than the NA rad - £150)
TT Radiator hoses (£100?)
Side mount intercooler and pipework (or front mount, but i'd say a front mount would be pointless on a standard engine)
First catalytic converter (if doesn't come with engine)
Perhaps an uprated fuel pump (can't remember if this is necessary, but i put a Walbro in when i did my swap)
There is also some wiring changes on the Aristo loom that will need doing. There's a thread on here about the VVTI swap somewhere.
Then you need to add in things like cambelt change, water pump and service items as you'd really want this doing as part of the swap, be daft not to.
2. A GTE engine will work with a W58 gearbox at standard power output, however if you plan to increase the power to BPU levels and beyond, then the W58 isn't really up to the job. Not sure if you'd need a TT manual gearbox ECU rather than the NA one.
3. For a competent garage that has done the swap before (which is ideally what you want) then i'd imagine you'd be paying in the region of 1.5-2k labour +vat (20+hours @£70 an hour)
4. See number 1.