Scrump - I've been in the situation where I've been the wrong side of the organiser and they start going round the other way and pick up all the latecomers - so much so that at one singaround I had to leave before it got to me as I was due on somewhere else.
If I'm asked to run a singaround I will take note of the early birds and ask them before going to the people who come in late, jockey for position, do their song and go! I explain my reasons to everybody - "you've just come in so I'll miss you out until Fred has sung" - which may be half an hour down the line. If they stay fine - if they get up and go - still fine.

I would imagine everybody has a list of songs that they are comfortable with and can be written in a small A6 size notebook (the list not the words) which can be referred to through the session without all the rustling of turning over sheets of A4 to find a song.

As for optimum number of people - depends how often you want to sing. If you're happy with one song then it's a time consideration to get everyone in. If you want to do more then I would think that half an hour between songs would be OK but if you reckon on 3 or 4 minutes per song then 9 or 10 singers is the optimum. Short of locking the door when more than 10 singers are in it isn't really practical.
A long singaround tends to get people coming and going anyway so you get a change of participents through the day.

Cheers
Mark