Proving that CFLs are closed under even-ness using grammars
Actually you can shoot all three qestions with a single stone.

Since you can easily define a regular language $Even=\Sigma^{2n}$ for all
even strings :


you prove the result by applying closure of CF languages under
intersection with regular sets.
You use the standard construction of such an intersection based on
CF grammar to get the grammar version of the proof.
You use the standard construction of such an intersection based on
PDAs to get the PDA version of the proof.


You have to know at least one of the two constructions, since it is
usually how the closure under regular set intersection is proved.

The purpose of the question is to check that you know the theorem, and at least one way to prove it.