I don't have any drawing knowledge, but I do know a little bit of photoshop and vector editing. Is it possible to draw lewd animations somehow with a mouse? For example in the similar fashion that Shadman draws. Are there any recommended programs for this?
You surely can technically draw with a mouse. But I would highly recommend you invest a few bucks in a drawing tablet (beginner ones go for 25$). With or without Mouse, a good vector Freeware is inkscape, a good drawing software is Krita for example.
I don't know who Shadman is, but if the art style you're going for doesn't have a lot of lines, I recommend CaCaNi, it makes the animation process much easier although it works a bit different than the other animation softwares.
I've drawn a lot of stuff using mouse with vectors in Paint Tool SAI. Of course, I sketched it by hand, scanned the drawing and only then I drew over it using the mouse, but still, I think it's perfectly doable even without sketches.