Left- and right-handed trefoil knot and its mirror image. I know that trefoil knots do not have a mirror image, but I also know that there is a left-handed and a right-handed trefoil knot. I have the drawings of them. Isn't this a contradiction?

What do you mean by „do not have mirror images“? The left handed tre foil knot is exactly the mirror image of the right handed one and vice versa. Therefore there is no contradiction. Actually, the tre foil knot is the easiest example of a chiral knot, a knot not being equivalent to its mirror image.