The H480 batteries will work on the H Plus as they do for the 520. The H Plus batteries, as well as the H520 ones, are NOT backward compatible with the H480 (Typhoon H, H Pro).
As for the C23... We will have to wait and see if Yuneec releases a version compatible with the H480. Out of the box, a C23 meant for the H Plus will not work on the H480.
Speculation abounds that Yuneec has stated or will offer a version for the H480. It will not be for the H520, at least not with the same product name/number. The E90 is already there. Rebranding is always an option, of course, to signify the various platforms.
If, for some reason, the E90 and C23 are completely different cameras, then we can continue the speculation that IF the C23 is much better than the E90, we can only hope it is ported over to the H520, even if only rebranded as an E90-II or something.
Jeff