I thought it was set a good while ago at first but it seems contemporary. Do they really still have Geisha who dress and live like that? There can't be many surely.
From what I've read, yes. There's this whole idea of the living cultural treasure thing in Japan, where you've got people whose job it is to carry on ancient ways or crafts and be visible doing so. So geishas walking the street and doing performances at festivals, traditional craftspeople, and so forth.
Is it set in that historical reenactment area of Kyoto? Seems odd how everyone is always dressed like they are from the Meiji period or older.
As above, the modern geisha do it as a full-time lifestyle until they retire. So they dress like that in public and are trained to speak in a manner that matches, which is probably where the awkward dialogue comes from. I can't imagine it's easy to translate the courtly/archaic/oblique phrasing well.