Answer
a.
The water molecules will donate protons to the ammonia aqueous molecules, forming its conjugate acid, ammonium ion, and $OH^-$.
$$NH_3(aq) + H_2O(l) \leftrightharpoons NH_{4}^+(aq) + OH^-(aq)$$
b. Ammonia will also act as a base, receiving on proton from the hydrogen chloride, resulting in $N{H_4}^+$ and $Cl^-$, the conjugate pairs of the reactants. The resulting products will form a solid ionic compound.
$$NH_3(g) + HCl(g) \longrightarrow N{H_4}Cl(s)$$
Work Step by Step
According to the Bronsted-Lowry theory, ammonia $NH_3$ is a base, and is able to receive protons from Bronsted-Lowry acids, like water and gaseous hydrogen chloride.