Difficulty to find any preimages $a$ and $b$ for given $V$ so that $H(a) \oplus H(b) = V$?
$ Pr(H(a) \oplus H(b) = V)$ is independent of $V$ For a good hash, as pointed out in the comments. Pick your input space to be the output space of SHA-224 so with probability $1/2$ (1) holds.

The range of $H$ is a group under $\oplus$. So (2) holds. 

3 won't hold by the same group property. Another $2^{112}$ trials will likely yield $a',b'$ satisfying (3) with probability $1/2$.