OK - you are correct that the bowl is too small. If it were me, I would be doing 100% water changes every day/every other day and add aquarium salt (don't remember the proper dosage,but you should be able to find it on here somewhere). Use the salt treatment for 10 days ONLY (it can have a bad side affect if used constantly) and ditch the Melafix.
And, yes, it looks like tail biting to me also - BUT, the clean, warm salted water will help prevent infections.
If the plant in there is/was silk, it shouldn't have rough edges. What is that other thing in there? Is that rubber/plastic/other?
I know you mentioned getting a Biorb, but one of the members on here had one for her boy and HATED it!!!
This is an EXCELLENT tank for bettas (I own 3 of them and LOVE them):
OR if you really, really like the looks of a "bowl", look for a 2 gal. glass drum bowl. Like this:
I suggest the drum bowl rather than the round because the flat sides make it SO much easier to work with in regards to a heater and filter (small internal).
Oh - something else you can do now to help your guy is some floating plants (ancharius, wisterea, etc.). They will help eat the ammonia and other nasties and help keep the water clean! :)
Hope that helps & keep up updated!