I'd guess it will be an all new design and the Z3 name simply because it will be a smaller car. I doubt it will have any relation to the old Z3 other than size.
I'd also guess either a fixed top or if its convertible, fabric, because a hard top convertible wouldn't work with the carbon fibre/weight loss ethos.
Time will tell... either way it won't be a car I'll buy, I've had my convertible moment, the next car will be back to basics.