What is the reaction between aqueous ammonia and salt solution?

What you are describing is a metathesis reaction or a double displacement reaction. In order to attempt these problems it is a good idea to have a solubility table available so that you can check the solubility of possible products:
Consider the example you have given: You know that a reaction has taken place because you have seen a precipitate so you know that an insoluble substance has been formed
Try an equation and se what happens:

Pb(NO3)2 (aq) + 2NH4OH(aq) → Pb(OH)2 (s) + 2NH4NO3(aq)

You see that the insoluble Pb(OH)2 is formed

If you are asking about a possible reaction between NH4OH and NaCl, there is no reaction.

Pb(NO3)2 + 2 NH4OH = Pb(OH)2(s) + 2 NH4NO3(aq)

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If the salt is the product of a neutralization reaction between a strong base and a strong acid, the resulting salt solution will be neutral. Example: HCl + NaOH → NaCl + H2O. If the salt is the product of a reaction between a strong base and a weak acid, the salt solution will be basic. Example: C2H4O2 (acetic acid) + NaOH → NaC2H3O2 (sodium acetate) + H2O. If the salt is the product of a reaction between a strong acid and a weak base, the salt solution will be acidic. Example: NH3 (ammonia) + HCl → NH4Cl (ammonium chloride). If a weak acid is reacted with a weak base, it's hard to tell what would happen. It would depend on the relative acidity and basicity of the reagents involved. However, if the solution does become acidic or basic, it will be only very weakly so; perhaps pH of 7 ± 0.5 or so.

Since you are combining equal moles of acid and base in reactions where you will get complete reaction of the products you should end up with a neutral pH in all of the above so only no. 3 is correct