I would start three weeks late. Plants will make up for it quickly once in the ground. Water needs depend on so many factors. I wouldn't want to try to gauge it from afar.

I always cover my germinating seed with a plastic cover. I save plastic carry-out containers with clear lids for that purpose, and plugs get set into a Perma-Nest tray with plastic lid. The lids keep things from drying out, and I never water anything in the germination tray before they come up (other than preparing the sowing medium, obviously). They usually take maybe a week or so to germinate but obviously some stuff comes up within a few days -- it's fine to leave the plastic lid on for a few days after germination, it will keep the moisture in. Not sure what you use as medium, but IME Jiffy pots are going to dry out a lot faster than a potting mix.

That said, I'm curious why you start peppers and tomatoes so early? Planting out time isn't until mid-May at the earliest and really it's best to wait until the last week of May because mid-May is iffy -- you're in OH, so thinking it is similar down where you are - ?. Are you using season extenders (e.g. wall-o-waters) to set stuff out in late April/early May? If not, sowing when you return at the end of March should be fine, you'll still get 6-8 weeks indoors, that's plenty of time for peppers and tomatoes.

To the extent they can be covered, that would do the trick. When I seed my transplant pots (paper cups, etc.) I ALWAYS put each in a plastic bag. Those long newspaper bags are perfect, if cut to size. They wrap around the base of the cup, and have many inches of space at the top for the seedling to leaf out. Once installed, you NEVER have to water until the plastic bags are removed. The soil never dries out. I leave the bags on for at least two weeks, during which time I might as well not even be there. Once the plastic bags are removed, yes, they have to be watered every other day. Be careful though, in that it can get warm inside those bags.

Interesting thanks! I have a large cold frame with heated soil cables so I can typically get things in the ground weeks earlier then everyone else.