First of all, use polycarbonate (Lexan) rather than acrylic (Plexiglass). It's much tougher and less likely to fracture from impact, from any possible holes from fasteners or from solvents in the calk attacking it at the edges. You can actually hit a Lexan window with a hammer and it will bounce off. Do not try that with plexiglass.
I think you're probably going to need some sort of low frame on the inside of the boat, similar to the one shown in the CLC kayak instructions. Any way you do it, it's likely to make a weak spot in the bottom to some extent, but if you stay away from shallow, rocky water it shouldn't be a major problem. I would not use epoxy for attaching the window. 3M 4000 marine calk or maybe 3M 4200 (both removable if ever needed) would be my choice and I'd probably countersink a few small holes and screw it to the frame from the outside of the hull over a generous bead of calk. If the frame and hull edge are well sealed with epoxy when constructed and the calking job is decent, there is no reason that it should leak at all.
I don't see any reason why the window needs to protrude from the hull. I doubt it will make any difference in visibility and it just exposes it to more potential damage. My Star sailboat had a Lexan window in the bottom, set flush into a frame so that you could see if there were weeds hung-up on the keel and it worked fine and didn't leak. The rag is probably there more for wiping consensation off the inside than for leaks.
These windows work, but aren't entirely problem-free. In cold water and warm weather you do get condensation at times. You also get a lot of reflected glare off of it if it's out in the open. The difference between what you will be able to see, looking down between your knees from a canoe seat and what you would be able to see if you, for example, were to lie in the bottom of the canoe with a light-blocking hood over your head and over the window is night and day.