Will otters mink muskrats use culverts with much water moving through them i see lots of videos of folks trapping in culverts but the water they are in is basically standing still.

They all do, though in the case of other and mink they'll go over them as well. Not always practical to set insude the culverts.

I know here otter usually go up and over the culverts instead of through them.

Some do and some don't.Very worth setting up.