I've taking over some reef tank duties from my dad which due to health issue can't do meany things right now. We have a main tank up stairs and a backup/emergency tank in the garage. We have this one coral that needs Id'ing. Also with the second image is this aiptasia?
Snap them off at the base and if you see any signs of webbing afterwards you can try kalk paste. They are relentless pests, I would rate them up there with aptasia.