Hello, and welcome to the forum! I'm sorry your experience with fish has been difficult thus far, but hopefully we can get things sorted out. I'll answer what I can, and leave it to the those more experienced with goldfish to figure out what's going on with your little guy.
I can relate to feeling overwhelmed by all the information out there. Different sources have different takes on how it is best to cycle. I'll give you my take on it; hopefully this will be helpful to you.
If I were you, I would get a larger tank (goldfish need a minimum of 30 gallons, bigger is always better). Goldfish just produce so much waste that it's difficult to manage in such a small tank. Once you've gotten a larger tank, you'd need to fish-in-cycle. It would be a great idea to get ahold of some filter media from an already established tank (whether that be from a friend or a trustworthy local fish store) to jump start the cycle. Just make sure the media remains wet with dechlorinated water in transit in order to keep the beneficial bacteria alive (tap water or drying out will kill it). Sometimes if you get enough beneficial bacteria, it can cycle it very quickly and drastically cut down on the time needed for BB colonies to build up.
I'll post a link at the end for you to read on fish-in-cycling, but it needs to be done carefully and parameters must be monitored with diligence. Make sure to get a test kit so you can monitor parameters and do water changes as needed. (A reliable test kit is the API Master Test Kit. Though it's a bit of an investment, it's definitely worth it for the accuracy.)
Hopefully cleaner water and more stable parameters will help your goldfish recover if it truly is a water quality issue.
With regards to the 2.5 gallon tank, you might be able to keep a betta in it, but personally I don't recommend anything less than 5 gallons for a betta. After moving a friend's betta from a 2.5 to a 5 gallon, the difference in his mood and activity convinced me that the 2.5 was just too small. In addition, small tanks less than 5 gallons can be tricky to cycle.
That said, you could use the tank for snails or a few dwarf shrimp. Both can be intriguing and rewarding to keep. A single mystery snail, a group of ramshorns, a pair of nerites, some red cherry shrimp, or possibly a single African dwarf frog could work (not together, just one of the mentioned groups, to avoid overstocking).
You would keep everything that's in the tank now; just make sure it properly cycles and it's good to go for new inhabitant(s).
I don't see any problem with your TopFin products. Just be aware that sometimes bacterial starters are not effective, as it is difficult to keep bacteria alive in a bottle; it can be exposed to temperature fluctuations and have died by the time you purchase it. The best way to acquire BB is to take seeded media from the filter of an established tank.
For your Ph, I'd wait until you have the API Kit and get an accurate reading before deciding if you need to adjust it.
I hope this helps! I wish you all the best in getting this figured out.
Here's the link, as promised. This is what I used when cycling my tank.
Fish-in Cycling: Step over into the dark side - Aquarium Advice