New Gardener! Growing Herbs From Seed

This is my first year growing herbs from seeds. I already have some herbs that I bought as small plants, and they've been doing well for a year or two.
I purchased seeds of chives, cilantro, French thyme, rosemary, Serrano chili peppers and jalapeño chili peppers. I used 5" pots and new potting soil. I sowed seeds into the soil on Sunday (it's Friday now). I watered the plants and covered them with wet newspaper, taking the newspaper off for a few hours a day to let them breathe before re-wetting the soil with a spray bottle.
So far, the French thyme has begun to germinate. These were very very tiny seeds, so I had just sprinkled them on top of the soil and pressed them down with my fingertips. The other ones I dug small holes for about 0.5 inches (1cm) down into the soil. Was that too much? None of the other plants have begun to germinate. If you could help with this I'd really appreciate it!!

I think you planted the seeds about twice as deep as they should have been planted. Most seeds should only be covered with twice their thickness of soil. If they have not managed to push through after about a month, very gently start to remove some of the top soil.
The rosemary does not germinate readily, but does best at about 65F (17C). Cilantro likes to be cool to germinate, so try a cooler spot. Chili peppers like heat and moving the pot over a radiator might be just the thing to get them to sprout.

Also, now that the French thyme has germinated, should I uncover it and place it in the window? I don't want to burn the little sprouts! Thank you so much for any help you may be able to offer!

Do the uncovering slowly, over a couple of days or more. Also move them into a sunny window-again slowly to avoid shocks. The more etiolated (skinny, reaching for light) they are the slower you have to proceed.