I guess you should know how to find and read a data sheet then. Check the sections on alternate pin functions.
I suppose Arduino.cc would be disappointed, but I have never owned a true Nano, only clones. Dozens of them. Scads of projects using I2C. Never have I seen one that didn't work. Ever.
From your project descriptions, I guess that you're probably overloading the Nano power supply.
Edit - there certainly have been pirated IC's with flaws. Generally, it is not so easy to make a fake, so in the quantities that must be made for the perpetrators to make a profit, most fakes are known and you can index them online. I may have seen 328 clones mentioned somewhere, but I can tell you that the price of real 328s in the say, 100,000's quantity, is so low that most "order online" Nanos have at least a genuine 328, even if maybe it is gray shift or "borrowed". So, it's possible you've been bitten, but some swapping with other Nanos would seem to be the key to being sure, assuming that is what you want to be.
WRT pinouts, I expect to see labels on the PCB itself that are accurate. I can work it out from there.