If I have an SSD boot drive, and I reset Windows on that boot drive (completely erase everything), does that affect any additional drives such as an HDD?
That depends, under normal circumstances, no. But if you have set up a RAID on multiple disks and SSDs and such, then depending on the configuration, it is possible that removing a drive or zeroing out a disk "might" make the other disk unsuable.
After resetting Windows/setting up a new boot drive: Do you need to partition the drive once more? Can you partition a drive more than once? Does partitioning a drive erase data?
Depends, on how you have removed a disk, like if you regenerated it, like written zeros from the very first sector of a disk to totally clear it then, yes you would have to repartition the whole thing and also generate a new fresh partition table. because everything including the partition tables and the partitions themselves are gone.
But, if you format every single partition separately, then only the content of that particular partition on that disk is gone, then you wouldn't have to re-partition the whole disk.
depends on what you do or mean by that.
So depends on what you mean by partitioning a drive and how you do it.
Can you swap the boot drive or swap a game drive (HDD) between PCs without conflict?
While I didn't understand what you meant by swapping exactly, but if by swapping you mean take out a "game" disk and use it on another PC, depends on a lot of factors. If the games are portable, if only the games installers are there or are the games previously installed on that drive, how the games work, and many other factors. Then there is a 50-50 chance the games will work if they are installed on that disk.
But if that disk only stores the installers of the games, then you can move it to as many pcs as you want. It would work, no matter what.
Unless it is encrypted or has some bounds to the current operating system, which might lock it.
So it still depends on the setup.
My instincts tell me that as long as you choose not to format those additional drives they'll remain the same regardless of the boot drive.
Yes while your instincts are right, it still depends on a couple of factors like the setup for example, the encryption, any other bounds that maybe in place, but normally, yes you are right.
I hope this helps.