its good that you have him in a good tank with a filter.
do you have a heater? without the correct warm tempurature, bettas are sluggish and slow and their colours disappear.
keep the tempurature between 76-84 degrees, the warmer the better.
you can cut the point if the plants have leaves, but if the plant is grass, then id remove it because ievn if you cut the pointy tip off, the long part could still get in the hole and rip it even further.
also you could go and get a small bottle of bettafix, which helps repair ripped and torn fins, along with rin rot.
hopefully it will regrow his tail. but you could do a salt bath, as they are known to work as well. good luck!