Translations marked with a ">" are incorrect. The comments after them attempt to explain why.
> ~Ex Ey Ez Eu[(x # y & x #z & y #z & x # u & y # u & z # u) & Aw(Small(w) -> (w = x v w = y v w = z v w = u))]
This says that it is not the case that there are exactly four things that are small. It doesn't really say anything about how many objects there are that are not small.
> Ex (Cube(x) & Large(x) & Ay (Dodec(y) -> ~BackOf(y, x)))
Close. Your sentence says there is at least one large cube with no dodecahedra in back of it. It should say that there is exactly one large cube and no dodecahedron is in back of it.