3D printer calibration test STLs?
Yes.

There are more test models one can download than would be possible to list here. A search on Thingiverse results in pages and pages of useful models. A common model for testing is called the 3d Benchy, although it is not particularly parametric. Overhangs, retraction, layer alignment and other aspects of your printer are tested with this model.

Another option is to purchase a set of test models from 3dkitbash.com:

QuickPrintTests

The models lists as such:

#3dk01 - Voids
#3dk02 - Spikes
#3dk03 - Flex
#3dk04 - Edge
#3dk05 - Text
#3dk06 - Bridge
#3dk07 - Dissolve
#3dk08 - Ball Joint
#3dk09 - Hinge
#3dk10 - Columns


which are more specifically defined for testing your printer. I would expect that Thingiverse and other model-sharing sites would have similar designs available to meet your specific requirements.