How does email communication with a private pilot affect FAA rules on compensation?
I'll answer it from the FAA since that's what I know.

The FAR is pretty clear on the matter here  


  (a) Except as provided in paragraphs (b) through (h) of this section, no person who holds a private pilot certificate may act as pilot in command of an aircraft that is carrying passengers or property for compensation or hire; nor may that person, for compensation or hire, act as pilot in command of an aircraft.


However if you want to split the cost evenly, you can:


  (c) A private pilot may not pay less than the pro rata share of the operating expenses of a flight with passengers, provided the expenses involve only fuel, oil, airport expenditures, or rental fees.


For what it's worth I would say you can still operate under Part 91 in the case you have outlined. 

Basically the FAA prevents a PPL holder from receiving any kind of compensation for a flight. This Article talks about some of the points that the FAA discussed when shutting down these services. The issue with some of these sharing services is that the middle man (AirPooler) and the like take a fee, this seems like the aspect that the FAA had an issue with since although the pilot was not profiting per se, someone was, this seems to be the FAA trigger. I don't know much about the deep aspects of the law but I'm sure there are things that can also arise with being a middleman/deal broker of these kinds of things.