Why is one switch hot wire black and another white?
Getting switch loop wires mixed up isn't any big deal.  They are both hot, just one is always hot and one is switched hot.  Since they are both hots,   the whites should be marked with tape at both ends.

It appears both switches are on the far end of switch loops, and may even be derived from different circuits, possibly on different poles (notice how the installer broke off the common tab on the old duplex switch).   So the easiest way to control them with one switch handle is a double-pole switch.  Fortunately these do exist in household form factors, such as this Leviton CAB2-20W, which is rated for 277V so it's good for opposite poles (240V).  AB goes on one pole, CD on the other.