Is black mold that is forming in our house safe?

No. Mold should not be growing in your home. There are several molds that are black in color and all could potentially cause human illness either as an allergen or a respiratory irritant for others. If mold is seen on a wall this often is due to a water leak from a hidden pipe and might require removal of the sheetrock to determine the source.
Hard to say. Mold can be an allergen or produce toxins. It can also be benign. Have the mold tested to see what species, then consult your physician.