1. For your FOL translation of 1, I would move a right parenthesis much farther to the right. That is, instead of
∀x (E(x) /\ ¬V(x)) --> ∃y (C(y) /\ S(x,y)
I would have
∀x ((E(x) /\ ¬V(x)) --> ∃y (C(y) /\ S(x,y)).
Otherwise, the scope of the x quantifier is curtailed prematurely: you need it in the S(x,y) predicate!
2. You haven't quite captured the nuance that for some of those drug pushers entering the country, they were only searched by drug pushers. You have also curtailed the x quantifier too soon again. Try this on for size:
∃x ((P(x) /\ E(x)) /\ ∃y (S(x,y) --> P(y))).
3. Careful with your parentheses. Look at this instead:
∀x (V(x) --> ¬P(x))
4. Again, careful with your parentheses. Try this instead:
∃x (C(x) /\ P(x)).
You can get prenex normal form quite easily for all these statements, I think. Once you get prenex, it shouldn't be too hard to get CNF inside the quantifier parts. What do you get?