Still worried about my betta!

Hi everyone!

New owner here, and still very much worried about my betta’s welfare. I bought a very sickly-looking fish so I’m not sure what’s normal behaviour for a betta, whether he’s on the up-and-up or if he’s still distressed. I’ve got a couple of questions I’m hoping you guys can answer! This might get a bit long.

First things first, the details: 2.6 gallon tank, filtered, no heater because I’m on a tropical island with a climate similar to Thailand (sweating as I type this!). I’ve got one plant, and a moss ball with gravel substrate. I’m pretty sure my tank’s not cycled, trying my best to find a water test kit locally but am planning on keeping up with 25-30% water changes every 3-4 days until I get one. (I’ve had my betta for 9 days now). I’ve attached some pictures I hope will help!

1. My betta has got clamped fins about 60% of the time. He relaxed them when I first transferred him to the tank, it’s relaxed when I feed him, he relaxes them when he sees me come up to the tank and it’s relaxed at other random moments when it seems like he’s ‘hunting’ around the tank. Other times he just floats or swims with clamped fins. Should I be worried, and what can I do to help relieve it?

2. Related to the previous question: Anytime he swims, his fins push really close to his body. Is this normal? Most other bettas seem to keep them upright even when swimming fast.

3. He has that streak across his body ever since I bought him at the store. Permanent stress streak? Part of his colouring? Still stressed?

4. The first few days in the tank, he seemed content to swim all over the tank and never went near the plants. Lately I’ve noticed he swims through the leaves, kind of hides between them and messes with the moss ball. Is he just getting used to the plants or is he scratching himself? (I have photos with the flash on, as well as with aquarium lights. I stressed out that he might have velvet, but perhaps it’s simply his natural iridescence? His colour reminds me of an oil slick, every time you tilt your head he's a different colour)

5. He seems to be very active but when I have time to watch him more, I’ve noticed he likes to lie on the gravel (sometimes in the open, sometimes wedged between the moss ball and the tank. Sometimes his fins are clamped, sometimes they’re open). Is this just where he likes to rest, or is he sick?

6. Recently he’s also been digging at the base of the plants and in the gravel. As I type this, he’s stuck (almost anchored) his head at the roots while his body floats around (fins unclamped). Any reason for this? Is it normal for a betta to hang out at the bottom of his tank or is he lethargic?

7. Is it weird that he doesn’t seem afraid of the filter output and of water changes? He’s always swimming under the falling water, drifts away and swims under it again.

Some good signs! He still eats like a beast (has a problem with his aim though), swims up to me like mad when I enter the room, will follow my finger if I place it on the glass (his tank is next to my computer on my table, and he seems to like to hang out on my side when I’m around).

My biggest worry is the perpetual clamped fins and that stripe, it feels like he’s constantly telling me that he’s unhappy! If there’s unusual behaviour in what I’ve described, or if you see something wrong in the pictures, do let me know! I’d like to fix it and have my betta as happy as possible! Thanks in advance for your help!

Link to album!