I planted thai chili pepper seeds today. The seeding soil is moist now. Should I water it if I see it drying out or don't water it until it sprouts? The seeding tray is open and not closed so air will definitely dries out the seeding soil.

Yes, water it. Keep it consistently moist but not sopping wet. You should also know that pepper seeds, especially ones like thai chilies, need hot temperatures to germinate. You should try to keep them at 90 degrees until they germinate. You might want to use a heating pad.

And some chilies take up to three weeks to germinate.