The brown ring test is used to detect the presence of which of the following ions?

Given below are two statements:
Statement-$I$: The gas liberated on warming a salt with dil $H_2SO_4$,turns a piece of paper dipped in lead acetate into black,it is a confirmatory test for sulphide ion.
Statement-$II$: In statement-$I$ the colour of paper turns black because of formation of lead sulphite.
In the light of the above statements,choose the most appropriate answer from the options given below:

Among the following observations, the correct one that differentiates between $SO_{3}^{2-}$ and $SO_{4}^{2-}$ is:

During the detection of an acidic radical present in a salt,a student obtains a pale yellow precipitate that is soluble with difficulty in $NH_4OH$ solution when the sodium carbonate extract is first acidified with dil. $HNO_3$ and then $AgNO_3$ solution is added. This indicates the presence of:

$S^{2-}$ and $SO_3^{2-}$ can be distinguished by using

$X + H_2SO_4 \to Y$ (a colorless gas with a pungent smell).
$Y + K_2Cr_2O_7 + H_2SO_4 \to$ green colored solution.
What are $X$ and $Y$?