Which one is the right design??(very simple design)

The compiler will tell you fmax (you don't need to calculate it). In the first case it gave you because there are 8 paths of direct connection between x and output.

In the second case there is no path to analyse between two registers.

Normally, all io inputs/outputs must be registered by user and all internal modules can be registered at outputs only since the internal inputs acquire

registers from outputs of previous module.

So you need to register the input, i.e. just insert your "q <= input" inside clocked process. so you are back to 8 more registers I am afraid. But when this module is part of longer chain of modules then you don't need to register the input.

You need to tell compiler what is your clock speed in the timing settings.