Restoring a neglected tank back to its former glory

Sixth (I think) 10% water change complete. I think I'm going to do one more 10% tomorrow then start 20% changes.
They're looking a lot more active and have much better colors than they did a week ago. I haven't checked their gills yet today to see if they're red or not, they probably still are but not as bad.

Also, is it fine to skip a single day of vacuuming? Or should I push through and vacuum it? Does it matter all that much?
If you don't have time to do a gravel clean one day it isn't going to harm the fish that much. After all, they have been living in the gunk for a while before now. However, if you are doing a water change, you normally use a gravel cleaner to syphon water out so you may as well gravel clean some of the substrate while you are draining some water.

But if you haven't got time, then it's fine to miss a day. The main thing is to try and do small water changes and gravel cleans for a few weeks to reduce the gunk in the tank and to slowly get the fish use to cleaner water. Then start doing bigger water changes less often.
Been a bit since I found time to update. I've changed the water almost every day the last week (2 weeks?) and it's really starting to look cleaner. The fish seem a lot happier.

I got pretty sick on Monday, so I missed Monday and Tuesday, but I did change it on Wednesday, Thursday, and Friday.

I think I'm going to switch to twice a week now, rather than daily. Next week I'm going to try cleaning the filter.
I cleaned the filter today. It took a few tries to start up, but it works now.

I've noticed bowing since the second or third month of having this tank but recently I feel like it's been worse. Is there anything I can do about it, or should do to avoid it potentially bursting? (I'll try to attach pictures)

(Ignore the messy house)
How long and high is the tank?
How thick is the glass?

An aquarium that is 2 foot long x 12 inches wide x 12 inches high, the glass on the sides should be at least 4mm thick, and the base should be at least 5mm thick.

An aquarium that is 18inches high should have 6mm thick glass.

All aquariums without a support strip/ cross member on the top of the tank will bow outwards to some degree. A mm or so is not an issue and is normal. If you are really concerned, you can lower the water level an inch or two and it will reduce the bend in the glass. However, lowering the water level will make it harder for external HOB power filters to take up water, so it becomes a balancing act. The water level in the aquarium should be high enough so the filter can automatically restart after a power failure, but low enough to reduce the curve in the glass.

If you have had the tank for more than a year, it should be fine.
Alright, good to know. It doesn't have a support strip. It's just about 20 inches long, 12 inches wide, 12 inches tall. I don't know how thick the glass is. I could measure it but I'm not currently at home. I'll do that later today.

I've had the tank for over 3 years, and it's done this since a couple months after setting it up, so it'll probably be fine. I did notice I think it's getting worse since I started doing water changes every day. I'll keep an eye on it, though.
It could be more noticeable now because the tank is fuller than its been for a while. I think the original picture you posted the tank was only about 2/3s full, whereas now it's pretty close to full.

Glass does slowly run and over a period of 20 years or so, the top of glass will end up slightly thinner than the bottom of the glass. This is more noticeable in long sheets of glass like a shop front, but it happens in all glass over time. However, a 3 year old tank that is only 12 inches high, it's not going to be a big issue. Just measure the thickness when you get home, if the glass is 4mm or more thick, then it should be fine.
Cleaned today! I went ahead and replaced the carbon filter, since I haven't been able to get the round sponge yet, and the filter wasn't letting anything through it. So it SHOULD be another month or two before I gotta replace it again.. hopefully. I'm getting to the point that I can't afford the new filters (since I'm 14 and have no income), so it'd be good to get the sponge soon.

I was once told you can use coal in your filter for the same effects as carbon. Is this true?
You do not want to use coal or charcoal in an aquarium because it is very alkaline and can change the water chemistry. Charcoal has been used in some situations to absorb chemicals in water but it is not very effective and Activated Carbon is a much better and safer alternative.

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