Custom Code Inspections

I'm relatively new to ReSharper but completely new to customizations, so hoping someone could provide some guidance here.  Apologies if I use incorrect ReSharper terminology here…

I'm interested in creating a custom Code Inspection rule which will do this:

1) Only apply the rule to a specific class in my solution.
2) Check to see if that class actually inherits from a specific base class.
3) Check to see if public methods in #2 actually extend methods defined in #1.
4) Check to see if the method in #3 are coded to be async.

I hope this makes sense.  Any thoughts or feedback is greatly appreciated!
Thanks!