ionization of H2SO4

HSO4- <--> H+ + SO42-
the reason that it is reversible is that it is more difficult to remove a proton(H+) from a negatively charge species(HSO4- ), backward reaction is favourable as well.
We still regard H2SO4 as strong acid due to the first dissociation of H+ from H2SO4 is complete. The second dissociation of H+ can be favourable if the H+ concentration is decreasing.One of the possible method is to add NaOH to react with H+ so that the equilibrium position shift to the right (i.e. forward reaction become more favorable for HSO4- <--> H+ + SO42-)

two steps in ionization of H2SO4 is a must as removal of first H+ is differ from removal of the second H+
H2SO4 --> H+ + HSO4-
HSO4- <--> H+ + SO42-
i hv explain why second ionization is more difficult as above.
i cannot follow your last question. but i guess you are asking if H2SO4 is dibasic it requires double volume of water. i think it is not true because water is always be in excess since it act as a solvent as well. water can change the concentration of H+(pH value by dilution but it won't affect the ionization of acid unless there is too little water to dissolve the acid (e.g use 1cm3 of water to dissolve 1 mole acid ---just kidding)