He is fin biting.. that isn't fin rot. No sign of rot on him at all.. just the common chunks taken out from biting.
He doesn't have dropsy, and unsure where got the idea he is constipated? He looks normal to me, body wise.
Melafix can be deadly to bettas if not VERY careful and you don't dilute it. There is an ingredient that can coat the labyrinth organ and cause suffocation easily in these fish.
I would remove 50% of the water today, add in the carbon filter, tomorrow remove 25% of the water, the day after tomorrow another 25% and then start on your regular weekly water changes. That should help clear out the Melafix.
He does not need salt.
He does not need medication.
He just needs clean water and good food..
Find out why he is biting his fins - could the filter be causing too strong of a current and making it difficult to swim? Sometimes they will bite off their fins to create shorter fins to make swimming easier on them - especially if they are new to larger tanks.
But he doesn't have rot, and he doesn't have bloating/dropsy and unsure why you believe he has constipation - just because you don't see the waste, doesn't mean it's not there.. the filter hides it in the substrate (why vacuuming each week is important).