White edges usually indicates new growth. This is fine.
Small tears, as you suspect, can be caused by his catching his fins on the plastic plants. You can get silk plants at Petsmart and Petco. Or, you can buy them online.
If you're into DIY projects, you can also make your own:
1) Buy silk plants from craft stores (Michaels, Walmart, etc).
2) Remove the leaves. You do NOT want to use any section that contains metal, such as the bendable stems.
3) Wash the leaves in hot water. Soak them overnight to remove any excess dyes.
4) If the dyes leach into the water, do not use the plants.
5) Assembly your plants. If you need a base, use a bit of aquarium safe silicone to attach the plant to a clean river rock.
6) Let it dry for at least 24 hrs before putting it into the tank.
- Silk plants (costs vary)
- River rocks ($1 at the dollar store)
- Loctite or other brand of aquarium safe silicone ($4.60 at Lowes)