Definitely the Z depth pass should be full precision (32bit) - all the Render elements under "Data" (Motion Vector, Position, Normal etc) should also be 32bit.
Exr is nowadays the standard for render elements and Tiff can sometimes be problematic. Exr is a pretty robust format.
The only caveat is that 32bit is overkill for the RGB and Lighting Render Elements, which can safely be 16bit, and there's no facility to change the bit depth per render element currently.