Mathman, here is the answer to your questions.
Most of the skaters for the Haydenettes come from here in town and from towns surrounding. If my memory serves me, there were some from as far away as southern NH and northern RI. Most of the Haydenettes move up from the junior and novice teams, The Ice Mates and the Ice Cubes.
The team is all women. I do not know if that is by choice or chance. I do know that there are very few male figure skaters in the Lexington area. I know a couple of people have asked me if I ever considered trying to joint the master's team. I'll ask Lynn Benson the next time I see her.
They train 11 months of the year, taking July off.
They don't tour per se, but do make a few appearances a year, such as at Rockefellar Center in New York and at some local ice shows, such as Ice Chips.
They are not paid. They do pay their way through fund raisers and the like.
It is a great sport and can only truelly be enjoyed seeing it live. TV doesn't do it justice. If my memory serves me correctly, I think synchro skating is going to be included in the next winter Olympics as an exhibition sport. If I am wrong, someone please correct me.
I hope this helps, Mathman.