Writing on the skin is not the same as tatooing, which is writing underneath the skin. As long as the skin is not punctured, and unless you are using something very unusual such as sulfuric acid to write on your skin, then no, it isn't harmful. It may not look very good, but it does no harm, and will eventually wash off.
No, it is not harmful.
No, Carbomer is not harmful to the skin. Carbomer is used to make gels out of liquids, but it doesn't interact with the skin when it's used on the skin.
yes very harmful
yes
Yes, drugs that can be absorbed through the skin can be harmful if not used properly.
yes it can burn and irritate skin...
no, if anything clay can make your skin softer
Yes they are harmful. Sun's ultraviolet radiations are fatal and cause harm to the skin.
Yes
UV radiation is harmful to skin. It causes skin cancer.
it can be harmful when rubbed against skin
Most likely, yes.