APFS compatibility with MacOS Extended (journaled) & external hard drive- help!

Your MacBook Pro will have no problem reading and writing to the external drive, regardless of how you format it. And for the purpose you state, that format should be Mac OS Extended (journaled) which will make it available to all three of your machines.

You say that you will be using this to transfer some data to the MBP which by itself would be fine. However, I would not use the same drive for data backups that I use for routine file transfers. It's just bad practice and risks a lot if the drive gets corrupted by unintentional misuse.

You didn't say which Seagate HDD you purchased and it doesn't really matter in this case except for the capacity. If you're going to use it for backups the capacity should be double the drive capacity of each Mac you intend to backup. For example, if each Mac has in internal drive of 1TB, then you would need a single external drive of 6TB capacity, formatted as Mac OS Extended (journaled) and partitioned into three partitions, one for each Mac. One great concern would be that having backups of multiple machines risks all the backups if something happens to that drive.

I would suggest that a better option would be an individual backup drive for each machine with twice the capacity of that machine, also formatted as Mac OS Extended (journaled) with a single partition. That you would use with Time Machine to backup the Mac and restore it if it ever comes to that.

In addition, I would also purchase another single drive formatted the same to be used anytime you wished to transfer data and files from one machine to another. The capacity of this drive could be whatever you felt comfortable with as regarding the sizes of the files you might normally move. Perhaps a 120 GB SSD.

And as far as the SSD v HDD choice goes... the SSD is notably faster to perform than an HDD, but for the purpose of doing regular backups, and HDD should be just fine.

Yes, there is a downside.

The old MacBook likely won't recognize a drive formatted with APFS. And depending on what the macOS being run on the others is they may not recognize it either.

APFS is the required format for the boot drive of any Mac running 10.15 Catalina. In addition, any Mac running macOS 10.13 High Sierra or macOS 10.14 Mojave can recognize and take advantage of the APFS formatted drive. Any previous macOS version will not know what to do with APFS.

AND... to be used as an external drive for a Time Machine backup, it MUST be formatted Mac OS Extended. (see the link above to Time Machine info).

Also, APFS is optimized for SSD performance, to be honest, and what value it brings to an HDD is something I cannot tell you, but I believe none.

edit - here's some light reading. File system formats available in Disk Utility on Mac - Apple Support

It doesn't matter. Just use Mac OS Extended (Journaled) for the HDD.

You don't have to have the same file format to back up.

APFS is a file system. It doesn't "read" anything. The OS reads the drives.