It sounds like a perfect mix. A bad battery that likely has a bad cell, corroded battery terminals that are not letting the battery charge properly. The fast clicking says the battery is at least very weak, however if it was that cold and the battery was already discharged it is likely that it also froze and shorted it internally, that is why the pack drained fast without starting it. If it still has the OE negative cable with the end like the one in the first picture you can replace that connector. Take a hacksaw or similar, no power tools that can create a spark though, you don't want to chance an exploding battery. Cut the terminal off at the line, then drill a hole to match the size of the bolt in a lead free terminal like the second picture. Bolt the terminal to the cable and install it. Clean up the positive terminal and after you install them both give them a coating of dielectric grease.
Now once you get it started I would run a charging system test to be sure the alternator is still okay.
https://www.2carpros.com/articles/car-battery-load-test
The reason for the load test is the way you said you needed to keep giving it more gas to stay running at times, low battery voltage can do a lot of things so it's possible the alternator is starting to fail.
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Monday, February 22nd, 2021 AT 1:04 AM