I don't think they actually flow from ocean to ocean anywhere; there's one which splits into a north and south heading river, but as far as I can tell none of them do impossible things. Could you explain what the issue is with rivers splitting apart? Plenty of real world rivers do this so I'm a bit lost as to exactly what you mean. Perhaps an explanation by way of example? If it's not too much trouble.
This is actually intentional; the borders are not fluid because they are decided upon by the imperial court and then given over to individual clans as opposed to being the result of conquest or what not. Each province is supposed to be roughly equal in population and wealth (except for the central urban provinces).
I tend to like such oddities in politics and culture and what not; to me they feel more plausible than having uniform and fully logical borders. Cultural and political enclaves are not uncommon in real history, and inserting little oddities like that in the map give a good excuse for building interesting setting fluff. I should also mention that these cultures are not necessarily as distinct as people may be assuming; rather than being the difference between say German and French culture, it's more the difference between say the culture of Paris and the culture of Marseille.Also, some of your cultural depictions, while not necessarily implausible, might raise eyebrows. For example, the enclave of Makanatari on the island of Zaisuke seems odd, unless you have an in-world explanation. There are a few other minor nitpicks I could mention, but I won't right now.
I know, that's laziness at work; I haven't seen fit to fix that yet.[EDIT: sorry, I had to nitpick. Couldn't help myself. First, it is unfortunate the way some of your rivers look when they reach a sea or lake (the river above Chotei shows it most prominently);
Yeah, those are bugs. I kind of rushed the cultural map with the geographical features, thanks for pointing them out.second, in the cultural map, the lake on Chuukonoke looks like some of the mountains are on it; third (and this is a really minor nitpick, but you wanted feedback, right?) the cultural map also shows some minor yellow bits on Chuukonoke, which I assume aren't deliberate. Those issues are really minor, and you can probably ignore them if you want, and the map will still look fine.]