The frog needs time to acclimate. Just give him/her a couple weeks. I lost a juvenile white's, only to find him 2 months later in my basement. So I can attest to the fact that they can go a while without eating.

As far as the water goes, he will not drown. As long as they have easy access to get out of the water, they will be fine. My male white's takes laps in their enclosure nightly. He swims for about 20 minutes then soaks all night and the water is much deeper than he is tall in parts.