Welcome to the forum and what a lovely Betta....
If she is otherwise acting, eating, pooping and generally appears fine.....I wouldn't worry too much...she looks more fat to me....I would cut back on the amount of food and fast once a week, increase the water changes to 50% with vacuum weekly...with that said...some of the signs and symptoms you posted sound stress related too....you may need to rehome the tetra-they will out grow the tank anyway and replace them with 3 more cory cats.....
With mixed species come feeding challenges too-Bettas tend to over eat and to feed the other species of fish and for them to get enough to eat especially the cory cat the Betta can end up over-eating.......
IMO/E your temp is fine-depending on your location you may or may not need a heater...your goal is to keep a stable water temp that doesn't vary much more that 5-10 degrees between day and night...try to keep it in the upper 70's range...you may find as she gets older that she will need a bit warmer water..
Salt-I would do some back to back 50% water only changes for the next 2 days and get most of it out....you don't need it and it could even be part of the reason for your Bettas edema...hard to say...but you also have cory cats and they don't do well in salt generally...but I have found that they don't seem to mind really small amounts short term
True, cory cats are social fish and do best when kept in larger groups...by keeping only one...it won't drop dead....but you will miss out on all the really neat behavior they can display and when kept as a lone fish they can become more stressed...safety in numbers....instinct to school...its just a matter of time before the stress of being alone gets to him/her.....by keeping a lone cory cat is not much different than keeping a Betta in a cup long term...IMO...needs not being met.....