I don’t think it is worth it. Once something internal breaks, it is really hard to fix. Unless you want to take the time to fix it, you should probably replace it. If you want to take the time to replace it, there are ifixit guides on this website.
That may be a problem with the eBay seller’s battery, and not necessarily the phone itself. Were there any other problems with the device during that month? Overheating, charging issues, phone crashing?
There may be a problem with your Airpods case then, and it probably can’t retain any charge, so, it only works when it is plugged in, when the energy is going purely into charging the airpods rather than charging the case.
Have you checked in the bios? You might need to brute format a version of your phone’s storage before you can be able to access any of the data, due to how apple locks down their lightning charger, and make it nearly impossible to transfer files from you phone to your computer, or vise versa.
Yes, it supports NVME, but, according to acer, it only supports ssd capacities up to 512gb. You can try with more, but I am not sure how successful it will be if you try, say, a Terabyte nvme or sata ssd. However, if you have the model with a hard drive in it, the hard drive can support 2 TB.