How to build a waterproof roof out of LEGO blocks? How would Lego blocks be tiled to provide a water proof roof against the rain?

The lattes or internal support structure of the roof doesn't have to be also made of Lego. Basically the tiles on a roof would be replaced with lego in such a way to be waterproof where the glue holds them together but isn't the water barrier.
Since you are willing to use a non-LEGO frame to hold the roof and glue to fix all together, I would recommend buying baseplates in bulk and gluing them onto a wooden frame as if they were shingles. If the gradient and the overlap (vertical between rows and horizontal between individual plates) are correctly matched, the rain won't get inside.

For more resources on professional shingle roofing see these links:

https://www.iko.com/na/pro/building-professional-tools/roofing-101/how-to-install-shingles/
https://www.wikihow.com/Lay-Shingles