Why Static Time Analyzer (STA) Engine doesn't show fmax for Fast Model?
Timing analysis is for checking for worst-case timing issues.  

For the clock period (setup time), you're interested in the worst case paths, the paths with the longest delay during the worst possible (slowest) operating conditions.  This requires the slow model.  

For hold time, you're interested in the worst case paths as well, but in this case you're looking at the shortest path, the paths with the shortest delay during the worst possible (fastest) operating conditions.  This requires the fast model.  

Checking setup times on the fast model or hold times on the slow model won't give you any meaningful information, because they are not the worst-case conditions for those checks.  

Edit: to your question on Vivado, it shows all of the standard timing information (worst/total negative slack, worst/total hold slack, worst/total pulse width slack) but it does not separate these out by fast model/slow model, it simply uses the appropriate model for each measurement.