well it depends on what charge Pb has. It could have a 2+ or 4+ charge.
To solve these problems you need the formula of the compound, and find the charges for them. Then you write out the equation and balance the charges for both sides. Then you balance the equation by making the elements on each side equal.
If it has a 2+ charge then PbSO4(aq)+2HNO3(aq)----> Pb(NO3)2(aq)+H2SO4(aq)
You could figure it out if the Pb is 4+ charge.
But i can't help you on the H2O + H2SO4.... but i know its a strong acid which means it ionizes 100% if that helps.