Serpents are symbolic because they have no legs? Or something else?

They're symbolic in a bunch of ways. Usually people think they're bad because of the serpent tempting Eve, but IMO that's wrong. What you've got there is a big hint - that was a symbol for infinity before it was secularized by making it a double loop for math. There's a lot more, though... The no legs part is about being in the material world, being lower