If you are already a PT user, the man page for this command gives very good explanations. I can clarify some of the points where I have got confused during my early working days.
1.) Looks like you are mixing set_false_path and set_clock_groups. Both of them are very different and typically you don't need both at the same time in a certain section of the design.
The whole idea behind set_clock_groups is to make timing paths go away (i.e. not show up in reports - so in that sense it is similar to false paths, but both these commands have very different purposes).
All 3 options i.e. -asyn -phys_excl and -logic_exl will cause no paths to show up. So there is no need for an explicit false path if you are able to use set_clock_groups.
2.) The differenece between -async and -log_excl is in the way, PT handles crosstalk analysis.
If 2 clocks are async, it means that they don't have any phase relationship at all. So instead of using definite timing windows based on arrival times/skew etc, the tool will use infinite timing windows when calculating aggressors and victims,
When you use -logic_excl switch, it still means that no timing paths will show up, however crosstalk analysis will be done with regular timing windows based on arrival times/skew etc.