I believe it was the first machine to have symmetrical encoding and decoding. Because it had a this property (as a letter was coded through the rotors, there was a rotor that reflected the encoding back through the rotor stages again), an operator could code and decode messages without reconfiguring the device.
Due to the fact above, the Enigma could never encode a letter onto itself. This greatly decreased the permutations allowed and made the device less effective.
I may be misunderstanding your cause and effect combination slightly here, but the symmertical encoding/decoding did not cause Engima to never encode a letter onto itself; that was specifically because of the reflector cog at the end of the wheels and the design of the electrical circuit within the machine.
Operators would encode the rotor setup in the message.
Twice (in case there were problems in receiving the messages); this led to the British and Polish (who never get enough public credit, IMO) knowing, for example, that if the message started 'ABCDEF', then A and D were the same original letter, and likewise with B/E and C/F. Herivel should also be credited with his work in predicting the rotor setups based on relatively simply psychology
Also, the Germans would include many standard phrases like praise for the Fuhrer.
Of more use was a certain weather station that broadcast messages at a set time every day and started each with 'WETTER'.
There are many simulators of the Enigma machine (see the Wikipedia article). Very cool to play with to really understand the operation of the device.
Writing one helps you appreciate it even more. Even the rotation of each cog isn't as simple as it seems.
