What can be logged as Total Time?
"Total time" isn't an officially defined term as far as I know. Most people seem to use it to mean "total flight time", i.e. the total of their PIC, SIC and flight training time (excluding simulator training).

In general, you can log and count whatever you want in your logbook provided that you log at least the items required in 61.51(a):


  (a) Training time and aeronautical experience. Each person must
  document and record the following time in a manner acceptable to the
  Administrator:
  
  (1) Training and aeronautical experience used to meet the requirements
  for a certificate, rating, or flight review of this part.
  
  (2) The aeronautical experience required for meeting the recent flight
  experience requirements of this part.


So, the bottom line is that "total time" is whatever you want it to be, and if you want to log 'fun time' in aircraft that you aren't qualified to fly then go ahead; the time just won't count for anything as far as the FAA is concerned.

As for your two scenarios:


You can't log any 'FAA time' because you're not certified to fly the
aircraft as PIC or SIC, and you aren't receiving training. You might note it in your logbook for your own reasons but you can't count it towards anything for the FAA's purposes.
You can't log 'FAA time' here either, for the reasons you mentioned. You're acting PIC for the entire flight, of course, but acting as PIC doesn't automatically let you log PIC unless other conditions are met. 61.51(e) lists all the ways you can log PIC time, e.g. sole manipulator, acting as PIC when more than one crewmember is required.