Black spots on leafs

That is thrip damage and the black spots are Thrip poop. 100% no question. Adult thrips lay eggs in the soft parts of the plant/leaves. Eggs hatch to larvae and the larvae literally suck the sap and sugars right out of the plants cells. ( This should leave marks on your leaves) The larvae then fall to the soil, to pupate. Once, they pupated, they hatch into adults with wings and a spikey abdomen, and crawl up to the leaves to start the process again. I haven't had much luck with soaps and neem oils because you need to saturate every part of the plant, and these guys like to hide in hard to get spots. Buy some Amblyseius cucumeris predator mites, they live soley on thrip eggs and larvae. Place these on the stems/leaves. Put Diatomaceous earth on the top layer of soil to prevent the larvae from pupating in the soil. Once you have the mites killing the larvae and eggs, and the diatoms killing the pupae, this should interrupt the cycle. In your second pic you can see the thrip larvae chilling in the vein of the leaf in the center! Best of Luck!