What precise hard drive do I need to install in this iMac?
I'm going to try to answer your question as best I can.


The drive is definitely a 3.5" SATA disk.
The notice doesn't apply to your model.
I'm not sure why the notice suggests to choose the same brand. For one, the drives are likely co-branded, with markings for both Apple and the company that made the drive. The companies that would have supplied the drives would be, AFAIK: Western Digital, Seagate and (possibly) Hitachi.
I'm not sure how similar you have to go in terms of storage. I'd guess you could probably use any SATA drive, but because of the temperature sensor, if I were you, I'd use one of the ones suggested in the guide, depending on your storage requirements (1-4TB).


TL;DR: If you're super worried about compatibility and need to get the machine working fast, disassemble it and look at the HDD to determine the brand, then order that brand. Otherwise, I would suggest you buy whichever of the listed HDDs strikes your fancy - I doubt that it really matters.