When should I notify ATC when I notice that I may have conflicting traffic? Let us say I am flying at FL100 with heading 360 and I noticed that ATC just cleared another aircraft to climb to FL100 with heading 270, and we may have a converging path if we proceed with our current flight paths; so, if, from then on, neither aircraft has gotten any further instructions from the controller, at what point should I remind ATC that I may have conflicting traffic based on my current flight profile and the clearance given to the other aircraft? For instance, would I have to wait until ADS-B alerted me of a loss of separation between me and the other traffic (say, coming within 3 nm of each other)? Or I could report the possible conflict earlier?
I think you will find there isn't a correct answer for this, and that answers will primarily be opinion based.  That said, my opinion is that if you have ADS-B, be patient and let ATC do their job.  

Speak up eventually, of course.  Especially if you see a clear converging path on your scope.  The 3nm you suggested seems like as good a point as any to mention it.

It's a little different if you are VMC.  In that case I might wait even longer and attempt to acquire a visual first.  That way your reminder to them can consist of your assessment of the need to deviate, or declare that you can maintain visual separation.