I doubt you can put a camera on a frog, unless it's very tiny and very light, otherwise they would be weighed down and it might damage their backs.
Most frogs that live in/near water, usually go there to either; eat,breed, or to escape predators[a safety zone]. Some frogs are primarily aquatic, like the ACF[African Clawed Frog], so they live in the water majority of the time. Frogs that are truely Amphibious[in the sense that they are comfortable on either land or in water] and don't live in the water full-time, usually go there just to do the reasons I listed above. Maybe even perhaps just chill-out, as they do frequently stay in the same spot for long periods.
Some frogs I think do sleep at the bottom, especially the Aquatic ones, like the ACF, and Frogs tend to be able to stay underwater for a long time, varying on the species and what environment it's built for. They can drown if they can't surface for air, so it's possible, especially for primarily Terrestrial species that can't swim as good.