You medium is saturated with water from what I can see on the pictures aka the soil is too wet , so a soil too wet can block the nutrients absobtion by the plant and create a nutrients lockout so she's not or she'll not be abble to feed herself.
The brown spots you're talking about are on the cotyledons , these spots are exactly where the shell of the seed where and sometimes it can do what you are seeing but it's not harmfull fot the plant and is not a sign of excess or def BUT if it continues to spread then my diagnosis could be wrong.
To water your seedling you can spray the soil instead of watering it , the process will be longer but like that you can't really end up with a soil too moist except if your hands are heavy. Watering a sedling can be tricky as it's easy to over or under water at that stage so the only real advise I can give you is to not stick to a water quantity to water but to the soil , and don't water too often it could keep a constant moisture in the pot and slowing lean to on overwatering