This thread has demonstrated that there are a wide variety of possibilities out there and we all have different ideas of what constitutes an ideal session.

Not only that, there are conflicting ideas as to what a session actually is.

In the strictest sense,IMO, it is a gathering of tune players and is predominantly instrumental although most reasonable people wouldn't object to the odd song here and there either from one of the tune players or a singer in the bar.
However, I realise that there are other arrangements featuring singer/strummers and so on which could be loosely described as sessions.
The important thing though is whatever arrangement you adopt, it should be as "unstructured" as possible. A scenario where everyone "takes turns" to sing a song or play a piece isn't really a session. Nor is picking tunes from tune books, song books etc behind the music stand and so.
It may be still be very enjoyable, useful, and worthwhile(I'm not going to knock it or suggest that such practices should be proscribed) but it's still something else.