Yes, very safe. There are many scientific studies done by research scientists which indicate a variety of dental benefits associated with fluoride and fluoridation.
Yes. Our teeth constantly lose minerals when ever we eat and pick them back up between meals. Small amounts of Fluoride found in water and toothpaste help teeth to pick up minerals and also make it harder to lose them. New teeth benefit the most. Despite lots of fear-mongering this small amount of Fluoride is perfectly safe. Proper amount is based on age so infants should not use Fluoride toothpaste.