No, the Apple iPhone 11 Pro Max does not support the Fingerprint Sensor as Apple has believed on its Face ID only.
Check Full Device Specifications Apple iPhone 11 Pro Max
Yes, the Apple iPhone 11 Pro Max is water-resistant as it comes with IP68 rating of resistant.
With IP68 water-resistant rating, it can survive up to half an hour submerged in about one and a half metre of water.
Check out this video for more knowledge about what IP rating is -
Check full specification of the device: Apple iPhone 11 Pro Max