Easy to do at home with a trolly jack and stands.
However you will have to gravity feed the gearbox refill if you do not have a transmission fluid pump.
A garage would probably charge about an hours labour circa £50,00.
More than likely the garage may not have got all the air out the system.
They are a bit tricky to bleed correctly if you are not conversant with the 350Z.
It is normal for gear selection to be easier with the engine switched off.
Nissan do not have a time or mileage for the diff fluid change, however if you are running a VLSD then I would recommend every 3 years or 36,000 miles, whichever comes soonest.
Alex.
No charge for diagnostics ? That will be a first from a Nissan dealership, so well done there.
Low mileage pre owned prop shafts are in stock and good to go same/next day if required.
Alex.
Yes, you have two wear and tear items on the compression rod.
The bushing can be replaced, however the ball joint can not as it is part of the compression rod.
Depends what parts are not fitted, however I doubt if reconnecting the battery will cause any issues.
You do not say but I am guessing that you want it live so you can lock the car ?
Guess that it is not the brake fluid level then.
Check your brake and high level rear light.
Just do the simple checks first as a process of elimination.