Your answer for C must be wrong, because the dimension of the space spanned by the vectors is only 2 (they all have zeros in the last component), but there are three vectors. Try to solve the linear system

for and . If you can find a nonzero solution, then your vectors are linearly dependent.

For E, what is the dimension of the space?

For F, I think your conclusion is correct, but I'm not so sure about your line of reasoning. If you include the zero vector in any group of vectors, you're going to have linear dependence, because you can set a linear combination of vectors in the group equal to zero, with all the coefficients of the nonzero vectors being zero, and the zero vector having any nonzero coefficient. Does that make sense?