Why is necessary to have a minimum thickness of material when doing testing?

Answer 1

Hardness testing cannot be done in thin materials, so they are processed to a bit different standard.

Hardness testing requires indenting the material with a known shape and weight of indenter, and then seeing what "indentation" remains when the load is removed. For thin materials, the indenter goes right through the material and tries to dent the test anvil (which is very hard). This will yield an erroneous reading.