The Courteous Knight is Child #112, more usually called The Baffled Knight; most versions don't involve anybody stealing a horse, though the dénoument usually involves humiliation; there's a whole family of French songs that tell the same story, so it's far from being a local issue.  The Farmer in Cheshire is a variant of The Yorkshire Bite / Highwayman Outwitted etc., which has been mentioned earlier; again unrelated, as is The Female Frolic (Sovay, etc).

There's quite a few songs involving female horse thieves.  The stories are all different, and mostly unrelated to each other.  Horses were important, of course, and songs about strong, clever and resourceful women have always been popular in Britain, which is how it should be, after all.