Fin rot or fin damage?


hello i'm new here. i just bought a 2.5" green spotted puffer yesterday.
i just noticed that the left pectoral fin is damage/chipped and a little bit more brown than the right side and the left pectoral fin is not moving when swimming.
also laying in the bottom of the tank 15-20% of the time and gradually more laying

tank information:
- 20 gallon
- hanging filter
- no lid
- air stone
- heater
- light
- white pebble substrate
- using seachem prime and stability to cycle the tank

in country that i live in, fish are very cheap, for example, you can get a 7 inch silver arowana for about $14
which some times can be hard to find good quality fish

also, i'm using additional bucket to cycle/grow nitrate
put water in, filter in, air stone, bunch of decayed shrimps , then put in seachem stability and wait for nitrate, and move the sponge filter from the bucket into the tank filter
so the tank water will look nice

1. how do i tell difference between fin damage and fin rot?
2. why laying in the bottom of the tank?
3. what should i do if its a fin rot?
4. green spotted puffer fish sensitive to light?
5. what should i do?
6. will the fin grow back? how long does it take?


Could we please have a photo?
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