Is frozen bottled water safe

Not really unless the ice is contaminated in some way.

Any drink that is overly cold, and especially if you drink it fast, can cause problems such as a "brain freeze". (Tip: breathe in and out through your nose in fast puffs if you get this kind of headache, the warmer air flow helps.)

When the ice melts in the milk, that does nothing but dilute the milk (unless, again, if the ice is made with contaminated water).

When traveling to some countries, it is best not to use ice cubes in any drinks because of the chance of contaminants in the water which could give you a food-borne or water-borne illness or could contain high levels of toxins or metals. Ask your travel agent for tips.