Question

What products are formed when aqueous solutions of NH4Cl and Pb(C2H3O2)2 are mixed?
Answer

NH4C2H3O2 and PbCl

NH4Pb and ClC2H3O2

NH4(C2H3O2)2 and PbCl2

NH4C2H3O2 and PbCl2

Answer 1

If any products are formed at all they would be
NH4C2H3O2 and PbCl2
but I assert that no reaction takes place unless the solutions are unusually concentrated.

Answer 2

Right. It is a double replacement reaction.

Answer 3

There would be a proton transfer from ammonium to acetate because acetic acid has a lower pKa than ammonium.