> Why not 'maen cylch' or 'cylch maen'?

The word 'maen' is singular, so that would sound weird. You'd want 'cylch meini'.

Welsh is such an old language so there are lots of ways of saying something like 'stone'. There are also distinct dialects remaining even today (North Welsh, or Gog as it's known by people further south, is very different to southern Welsh) so one word will be prevalent in one area while another is prevalent elsewhere.