Oof. I am sorry, and good luck to you and your plants! I don't know about the black spots - maybe a disease? maybe not much to worry about? try gently wiping them with rubbing alcohol to find out if they're lesions on the stem itself or some kind of surface residue/sooty mold - but my plants tend to lose leaves and flowers when they're under attack by insects. Have you checked under the leaves for anything like whiteflies/whitefly eggs, or aphids, or scale bugs? If you see a ridiculous number of ants climbing up and down the stems, that could be a tipoff that they're farming sap-sucking insects.
But I did notice that the leaves in the second photo look really crinkly. Unless that's normal for your plants, I'd give them a bit more calcium. It's probably not the cause of the leaf/flower drop, but in moderation, it probably won't hurt and may make them happier. (My habaneros usually get crinkly leaves when I've forgotten to give them their vinegar-dolomite solution recently.)
Not to throw lots of questions at you, but other things that might contribute to the leaf/flower dropping - how's the weather?
(Also, you can probably get away with giving your plants straight-from-the-tap water instead of distilled, unless your local tap water is really a nightmare. If over-chlorination is an issue, you can always leave a container of water out in the sun for a few hours to let most of the chlorine evaporate. Not that distilled water would necessarily hurt your plants, it just tends to be much more expensive than tap...)
