No. Natural sea salts are rich in iodine, so it doesn't need to be artificially added in. Commercial refined salt is stripped of all it's minerals, chemically cleaned and bleached. The iodine that is added is synthetic. An anti-caking chemical is also added that can build up in your organs causing problems. Stay away from refined table salt.
Iodine is an element. There is no such thing as "synthetic" iodine. One iodine atom is just like another (different isotopes aside). The human body cannot determine the source of an iodine atom.
Seawater IS rich in iodine ions, so salt made from seawater would likewise be rich in iodine. The rest of your contentions may be true. I don't know.