I can only speak for mathematics. At Harvey Mudd, students are required to write a senior thesis, which typically involves a lot of looking into the literature and at least a little bit of original research. Professors are selected for their ability to supervise undergraduate research. If you're not outstanding at this, you don't get tenure there.

They don't offer graduate programs, but it's usually considered a good idea to do undergrad/grad/postdoc at different schools anyway. Some of their students do go on to grad school, and they're typically well-prepared for it.

Can't speak to the rest of your questions as I don't know.