Aquarium salt should only be reserved for incidents of mild ill-health. Using it all the time builds up an immunity so it's useless when you actually need it. That, and the fact that bettas are freshwater fish, long term use of aq salt can be irritating to him. The recommended dosage of aq salt for bettas is for a maximum of ten days. It would be better to stop using it immediately, and keep it on hand in case he ever gets external parasites or fin rot or something.
I'm sorry, I thought you said cory cats!! I have no idea if oto's suck on fish. Something tells me they do bc I vaguely recall my sister telling me about her oto taking down a barb or something.
Missing chunks and threads could still be fin nipping if he did a messy job. Yes, unfortunately some bettas just bite their tails. It could be for making swimming easier (which makes sense when you look at a heavier finned betta compared to their short tailed wild counterparts). It doesn't sound like your fish is bored, he sounds like a very integrated part of the family! Both my veiltails bit their tails for different reasons (Lakitu bit bc the air bubbler in the tank freaked him out) (Ludendorff bit bc he was bored and lonely, and stopped altogether when I divided the tank with Bowser).
Despite what we're constantly told in media and pet store staff, bettas are quite social. They enjoy spending time with their humans and, as myself and a lot of other members have noticed, interacting with other bettas. Keeping a divider is not for everybody, for example it's a little ugly, but I can vouch for a marked increase in fish stimulation.