Columns instead of rows
 

How can I make my categories go three across, break, then another three, and also the files page show three across, break, then another three?

See attached for what I am after.

That would probably take both code and template edits. For the code edits, the PHP modulus operator can be handy, and for the template edits, that just takes time to format things how you want. Sorry but I'm not up for doing these things for you, as customizations really fall outside the realm of support, though you might be able to find someone on vBorg to do the changes for you.