Sorry this forum sometimes isn't the best place for a straight answer!!
Your questions :
How do I find this information without actually being there? - try Nailsworth Tourist Info Office on 01453 839222
Is there a local centre for classes e.g. astrology, yoga, French etc? Yes couple small community venues, range of classes, some run by Stroud College. Again tourist info should give you details. Ruskin Mill College in Nailworth also run a few classes that tend to be less mainstream.
Is there a cinema or film club? Yes Film club runs sometimes at primary school (I think?) Lovely little cinema at Wotton -U- Edge, not too far away or bigger cinema in Stroud.
Is there a good independent or community-run coffee shop? - Loads
Where do people meet for local events? Are there any local events? Loads - various things are put on in local village pubs, community centres, The Arkell Centre, Horsley Village Hall, local park for family fun days, firework night etc. Big Christmas event takes over whole of centre of Nailsworth one night at the end of Nov.
Is there a local farmers' market? Yes and its great!
Is there a sports centre and swimming pool? Yes little sports hall next to boys club, big gym at side of forest green rovers, tennis club by park. Swimming pool at Beaudesert school or Stroud, or Dursley.
Is Nailsworth a Transition Town? - I don't know what this is but its a welcoming town with plenty going on!