@DunderMifflin, there are a number of posts from the last few weeks further up in this thread that should be helpful to you.
Yes. I just did it, and several others have, too. A print-out of the Resident Authorization certificate PDF is equivalent to the physical Gold Card for border-crossing purposes.
I am not sure exactly where you are seeing this, but it is incorrect. Many people have verified their passports in their home country, then picked up their cards in Taiwan.
No. The authorization PDF is equivalent to an ARC for border-crossing purposes. It actually says “外僑居留證” (ARC) on it. Those with ARC do not need a Covid test. See the PDF Regulations of Citizens/Non-Citizens Entering Taiwan.