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Regarding the tetras, there could be a few reasons why the tetra keeps pushing the other into the corner. My guess would be it's either....
1. (Most likely) The larger tetra may just be establishing it's role (like being dominant) in a pecking order. If this is the case, the behavior should go away in about a week or so.
2. The tetra may be stressed due to not enough room in the tank, I'm pretty sure the red eye tetras require at least a 20 gallon (and so does the goldfish for that matter), but having them in this 10 gallon temporarily shouldn't be too big of a problem as long as you can upgrade soon.
3. The tetra may just be a bully. Like humans, all fish have different personalities, and some of them thrive on picking on other fish. If you find this cornering behavior doesn't stop soon (say after another week), and if you still have the receipt, I suggest taking that tetra back and replacing it with another one (perhaps a smaller one).
I know you didn't ask about this, but I'd like to give you a heads up. If you're going to keep a goldfish with these tetras (not recommended), your tank is going to require frequent or major water changes. Goldfish produce a lot of waste and therefor can spike the ammonia levels in your tank which could result in dead fish. I would personally recommend at least a 20% water change every other day, or a 50-60% water change once a week.