Enumerate probabilistic and other kinds of Turing machines together
When we talk about the enumeration of TM's, do we mean the "regular" deterministic ones?


We mean an enumeration of whatever kind of Turing machines we're talking about at the moment. Unless stated otherwise, "Turing machine" is normally taken to mean deterministic Turing machine.


  Perhaps one could think of a way to create some universal coding of TM's to strings that works for all different kinds of TM's?


There's no fixed list of "all different kinds of TM's", so I don't see how this would be possible.


  A related question, does a TM know it's own description?


It's not clear to me what it means for a TM to "know" anything.  A Turing machine is just its state set, transition function and so on.