Do I wait for the first coat of paint to completely dry before I put on
the second coat? Would this take a few hours, or should I wait a day?

And when I'm applying the second coat, do I cut in around the edges and
walls first with a brush, like I'm planning to do with the first coat
of paint? Or should I just use a roller the second time around and
paint as close to the edges as possible (would that cause lines to
appear between the first and second coats around the edges because I
didn't cut in)?

Apologies for the ignorant novice questions; I've never painted before.
I tried asking the sales clerk at the paint store for advice about
these details, but he more or less doesn't know (and unfortunately,
doesn't care, either).