Our nine-year-old daughter has been on a swim team in the US for three years. She wants to continue when we move to Zurich. Is there anyone on the Forum who swims for a team in Zurich (Limmat Sharks?), or knows someone on the team? Any requirements (Swiss citizenship?) besides swim skills?

Best thing would be to go to your local pool (Hallenbad (indoor pool), this time of year - Freibad (outdoor pool) would be closed!).
Each pool I've visited while here appears to have it's own swim club, although some may be affiliated, so you can get some details direct from the pool.
As for requirements, some of them (possibly all) would require an application that included a doctor's certificate saying that your daughter is healthy enough to swim.

Nah. The whole region is crawling with foreigners who swim in clubs, to say nothing of the coaches, many of whom have funny accents too. Competition licences are different and there are rules for swimming at the national championships but training, as far as I know, should produce no complications.