You fly a "Zero Lift" A of A which would be zero on an aircraft with a symetrical wing, or slightly less than zero on (i.e. a slight negative A of a) on an aircraft with a cambered wing.
As most aircraft have a positive angle of incidence, the deck angle would be slightly nose down, rather than pure vertical.
as IAS would mean TAS increases in the climb.
Yes it does, because drag
decreases with altitude due to lower air density. Thus for a constant thrust, a constant IAS but increasing TAS would result. (However, as most types of engine reduce in power with altitude, this doesn't seem likeley!!)