I seem to be having two separate problems. First problem is as demonstrated in the above video. When I start the car everything is fine, then when I either use "wash" or turn on regular wipers they go completely insane even on lowest setting. This brings us to problem two.

While active the wipers will go maximum full force crazy speeds (not in the video). When I turn the wipers "off" they keep going full crazy speed, and only after a random long time do they "stop". Once "stopped" they forever go up/down in little jumps as seen in the video. Once I use the wipers again, the process repeats forever, and my wipers never turn off unless I let the car sit for a few hours.

I've read something about taking apart the wiper motor and checking some kind of arms movement, but I have no idea what I'm doing with any of that. Advice is much welcome.

Found these two wiper motors (1, 2) on carparts.com. Note I do not have a wash fluid basin anyway so I have no use for the washer.