I've got the key to the wells, and wanted to use the one in by the statue, with a samurai guarding it - but the only gate leading there doesn't even seem to be possible to open (as in, it's not an interactive object) and so I can't get Takuma there (everyone else was able to climb around).

Link: http://i.imgur.com/0LLy85W.jpg - this is the gate I'm talking about.

To me it seems like the ox might be the key to opening it (annoy it so that it breaks the cart, and all the barrels crash the gate?), but I kept throwing rocks at it, and while it was kicking the cart every time I did, nothing else happened.

How do I get it open?
(or is there some other way to that well, that I missed?)

I tried the exact same thing when I played through the mission, but I'm pretty sure you can't break it or the ox is a rather stubborn one.

What you might want to check with Takuma, would be a bit more towards East from that gate. There is kind of a shooting range/practise area that helps him up to the upper level. It'll lead to the same place where you got the key from.

EDIT: ..East when looking from the original camera angle when starting the map, slightly North-West from your picture.

Yeah, I found out about the same route since posting.

Thanks anyway, though. :)