, so your base for U is correct.
For V,W, the bases you provided are wrong; consider this: What is the image of ? (There is none, so these bases are wrong!)
The correct answers would be:
Can you see why these are the answers? I'll expand if you want me to.
U+W is not direct as and
V+W is not direct as and
V+U is a direct sum. Let us assume there exists a non-zero shared element between them, then:
so, assume , then , then but then and then
Q. (c): , ,
Yes, it is correct that if and A,B are subspaces of , then
Can you follow from here on which two spaces give the answer?