Starting out on a side note- did you remove the salt that you placed in the tank? If not, then I would suggest doing a few water changes daily over the next few days to help remove it as prolonged exposure has potential to harm the kidney's/liver and potential to slow regrowth of fins.
As mentioned before, tank mates won't work well in that tank- the bio load will be too great, and placing multiple fish in that size of a tank will cause them to feel "trapped" as male bettas are territorial. Small schooling fish can also cause some bettas stress with their fast swimming. (Also, neons and most tetras in general like to nip fins, so in a smaller setting it just may be too stressful to have multiple fish.
But you can definitely try a snail or ghost shrimp in there- a lot of bettas enjoy watching snails, and a lot enjoy chasing down the shrimp. If you decide to go that route make sure to do some research (snails especially as most if you have multiple snails will end up breeding too quickly) and make sure to add in some easy to care for plants like Java grass (low lighting, don't need substrate, etc) to provide food for the shrimp/snail. The plants will also help provide extra coverage for shrimps.
As for why he is biting his tail.. could be almost anything, and could be nothing you have done/are doing at all. Usually stress is what causes them to bite their fins, or in cases such as halfmoons- too much drag caused by the large fins. Sadly, what we find most appealing is not natural to a betta and can be quite uncomfortable.
Since you've had him for a while we can rule out that he is building up his muscles from being in small spaces from the breeder.
You can add in more plants, but that may make him worse.. I have a male that if anything in his tank changes at all then he bites his fins. His tank has to be bare bottom with minimal decorations and only the decorations that he has had in his tank since day one. Some reason he latched onto the items that were in his hospital tank I placed him in after purchase and if anything changes he terrorizes his fins. So the smallest thing can cause them to stress enough to bite their fins..
The only thing you can do is try to think of what it could possibly be that is stressing him.. how long is his light kept on at night? Has it changed recently? Has your water change routine (how you go about it) changed recently? Any new items placed in the tank? Anything taken out? Find the cause and you may be able to reverse this habit, but don't expect to stop it as majority of these habits are habits for life.
Fish don't think like us, nor like dogs.. yes, mental stimulation keeps them moving, interactive and overall healthier.. but they don't get "bored" in the sense that we understand it. So I wouldn't worry too much about him being bored or lonely.. bettas are solitary fish, prefer living alone for the most part. What you can try is the mirror exercise, once or twice a day for 3-5 minutes show him a mirror to get his "blood pumping" and feel as if he "protected" his territory. Interaction with their owners or seeing other fish is very good for them.. too much alone time they can get stressed (this is where the "for the most part" comes in.. they want to live alone and be alone most of the time, but overall do want to see another betta from time to time). I have an old male that if he is taken away from the other bettas for any extended time will take out chunks of his fins.
Sorry for the long read, but what it comes down to is: sometimes you will figure it out, and sometimes you won't.. and even if you know what it is, doesn't mean you will be able to stop it. Le sigh... sill fish.