Do garden gnomes have their own folklore? Or is there anything similar to one?
They certainly do! Or at least they have folkloric origins.
Garden gnomes in the literal sense come from Germany, where the more widespread fancy of keeping little decorative statues in your garden muddled nicely together with the Northwest European notion of having gnomes (or tomte or kabouters) as helpful little creatures around the house and garden.
These creatures were usually male (or genderless but presumed male) and were loyal to a household, provided they were treated with respect. Usually this meant not spying on them and leaving some food out for them.
I’m Dutch and over here when we say tuinkabouter (garden-gnome) we mean a statue in the garden, but huiskabouter (house-gnome) refers to the old belief of having a kind little human-like figure living in your house. They are usually about the size of your hand, dressed neatly, with pointy red caps and a white beard. The German variety is much the same and while the Scandinavian types can differ a bit, they are clearly friendly cousins. Most of them are reported to be unusually strong for their size and capable of turning invisible.
I’ve written more about these household spirits in various cultures here. ^^