I have also kept both kuhlis and cories together for years and never had an issue. They are both peaceful, and frankly rather oblivious, so they are fine.
Yes, 5-6 cories will be fine.
I have kept a group of mixed cories. In my experience, they will hang out with similar looking cories, but they won't really formally school. I never had an issue with a mix though, so I think it is fine to have a few of one species and a few of another.