The 5D Mark III is weather-sealed against dust and moisture, making it splash-resistant, but it is not waterproof and cannot be submerged.
No, the Canon 5D Mark III has a maximum video resolution of Full HD (1920 x 1080) at up to 30fps.
It is compatible with all Canon EF mount lenses. It cannot natively use EF-S lenses (designed for crop sensors) or RF lenses (designed for mirrorless).
The LP-E6 battery provides approximately 950 shots per charge according to CIPA standards, though this decreases when using Live View or recording video.