Can OS X 10.5.8 be installed on a 2.3 GHz Intel Core i7 Mac Mini in order to upgrade to OS X 10.6.3 server? (The Goal: to quit 10.8 Server in order to use Rosetta software again)
Your Mac mini is probably a Apple Mac mini "Core i7" 2.3 (Late 2012) Macmini6,2. It was originally delivered with Mac OS X 10.8.1.
Neither 10.5 nor 10.6 contain the necessary drivers to support your hardware (especially USB3.0).
No. 10.5 doesn't include the necessary drivers for your machine, neither does 10.6
One option would be to install 10.6 Server in a Virtual Machine. There are a few tutorials on the net, it can be quiet tricky as I recall but it works.