Does my betta have fin rot?

[Here19]

I've had my betta, Lapis, for a week now and I'm worried that he might have fin rot. I don't know if I'm just paranoid or if he really has it, and all the pictures I've seen online don't exactly confirm whether or not he might have it.

He's eating properly and is curious. He has quite a bit of energy and will swim around the tank. He blew a bubblenest a few days back. He comes to greet me whenever I walk in the room or peer at the tank. Recently, he takes food out of my hand and has let me touch him a few times. Overall, he seems like quite a happy betta. Here are some pictures of him.

http://s1076.photobucket.com/albums/w449/Here19/

I think the first picture is the one where you can see the fin the best, but the other ones have different angles. I did my best to get some pictures, but because he was moving around so much, they all came out a bit blurry and dark, but I hope you can see his tail. I'm noticing that with his tail fin and the one around his belly has some redness to it. I can't really tell if that was there before, but to me it seems like the redness looks sort of like veins and just got there recently and is spreading. The ends of his tail fin doesn't seem frayed or damaged, but it's a little grey and red and seems to be going transparent. Again, I don't know if I'm paranoid or not.

I asked my dad his opinion which was a mistake. I have a pretty small unfiltered tank, so I was thinking of doing full water changes every day for a few days and see how he does, but my dad went and said that if I did that, I'd essentially be killing him. I don't think that's true, considering the fact that I want to keep toxins down, but I'm just worried about his fins. Both my parents think it's nothing, but I'm concerned.

Can you tell whether he has the beginning of fin rot? If he does, can you please tell me how to handle it and make him better?

Please help! Thank you!

Housing
What size is your tank? 0.5 gallon
What temperature is your tank? Approx 79 F
Does your tank have a filter? No
Does your tank have an air stone or other type of aeration? No
Is your tank heated? Yes
What tank mates does your betta fish live with? None

Food
What type of food do you feed your betta fish? A Nutrafin basix betta food
How often do you feed your betta fish? Twice a day

Maintenance
How often do you perform a water change? Once 3-4 days
What percentage of the water do you change when you perform a water change? 100%
What type of additives do you add to the water when you perform a water change? Nutrafin Betta Plus conditioner

Symptoms and Treatment
How has your betta fish's appearance changed? The look in the pictures
How has your betta fish's behavior changed? Been no change
When did you start noticing the symptoms? Right after the 4th of August
Have you started treating your fish? If so, how? No
Does your fish have any history of being ill? I just got him not too long ago.
How old is your fish (approximately)? No idea. He's spent a week in my house.

[MadameDesu]

The pictures make it hard to tell for sure. I can't really see any tears in his fins.
If you suspect it could be, then do daily 100% water changes using a good conditioner like stress coat. Maybe even treat with some AQ salt.
It sounds like he's doing well as his behavior is normal.
It's ok to feel a little paranoid in the first few weeks. I worried about my betta constantly in that time. The first time I saw her poop, I though she had a parasite attached to her lol