Is there a reason those aren't just cemented PVC pipe?

Compression fittings. Obviously so the plumbing can be disassembled for
repairs. Pumps often require removal for service. Take it apart and
replace the gasket if deteriorated. Reassemble *with some O-ring lube* and
you won't have leaks. Lubed compression fittings will tend to telescope
out, so make sure the assembly is held together by something other than the
friction of compression joints (friction you will no longer have).

2) Second, my sand filter had the small drain hole removed at the
bottom by the person who closed the pool. When I put it back in and
turn on the pumps there is leak from that hole. It looks like it was
caulked or had some other sealer put on there in the past. Can I just
caulk it with a kitchen/bath caulk to patch the little hole where the
screw in drain plug doesn't fit?

Use Teflon tape. Check the fitting isn't already cracked there from
overtightening.