Dear Ian,
firstly, a big congratulations on finishing your car and getting it registered!
I bet your first drive was exciting and that view down the bonnet is something to savour!!
I think you'll get used to the front mudguards bouncing around which, so long as they don't fall off, is quite normal and nothing to worry about.
From memory I used to run with tyre pressures around 18-20 psi and only a couple of clicks from full softness on the front shocks.
I'm not sure about the vibration but perhaps you've flat spotted your tyres on your first lap (...well that's what they always say on F1 TV
)
At least we finally know that gearbox works okay
Happy motoring.............peter.