2 smallish adults in the back of a GT is no problem, so a baby seat in the back shouldn't be an issue. You may have to bring the front passenger seat forward a bit, as a baby seat brings forward & raises the position. Unless the person who will be in the front passenger seat is really tall, I think it should not be a problem.
Motorway mpg should be in the mid-40's & even in town, it rarely drops under 40. Yes its reliable, at least in the 2 years I've owned mine. (06 model, 36k on the clock). Check the cambelt has been replaced, with documentation to prove it if the GT is 5 years old or more.
The boot should be big enough unless the baby buggy is enormous.
It will be a very different drive to a TVR, but then you could say that about just about any other car.
Oh, & get a remap. Mine added 30+bhp & loads of overtaking torque, with NO downsides.