Fin Rot, Teared Fin or Tail Biting?!

I am new to betta fish keeping, and my first betta lasted a week (swim bladder or strong filter). I got my second betta from Petco and I noticed the tail was rounded when it is supposed to be spiked, he is a crowntail. A few days later a small chunk seemed to be missing.







Housing
What size is your tank? 2.5
What temperature is your tank? ?
Does your tank have a filter? Not at the moment
Does your tank have an air stone or other type of aeration? No
Is your tank heated? No (House temp at 79)
What tank mates does your betta fish live with? None

Food
What type of food do you feed your betta fish? Hikari Gold
How often do you feed your betta fish? 6-8 a day, Fast on Wed.

Maintenance
How often do you perform a water change? Not enough time to tell
What percentage of the water do you change when you perform a water change? 30%-40%
What type of additives do you add to the water when you perform a water change? Aqueon Betta Bowl Plus

Water Parameters:
Have you tested your water? If so, what are the following parameters?

Ammonia: ?
Nitrite: ?
Nitrate: ?
pH: ?
Hardness: ?
Alkalinity: ?

Symptoms and Treatment
How has your betta fish's appearance changed? Not enough time to tell
How has your betta fish's behavior changed? Not enough time to tell
When did you start noticing the symptoms? Since I came home with him
Have you started treating your fish? If so, how? I don't Know how
Does your fish have any history of being ill? Not enough time to tell
How old is your fish (approximately)? It has been 5 days since I got him

I don't want to lose another fish!