> 1) Is this possible to do?
Yes....
> 2) should I do this on this EHD or something else?
I would normally recommend separate drives for each computer, but sharing a drive is doable.
There are a couple of ways of doing it. The 'easy' way is to alternate which computer the drive is plugged in to, and leave it plugged in long enough to finished backing up, then unmount it, unplug it, and reconnect to the other machine (you can see why I recommend separate drives).
An alternative would be to connect it to one machine and configure it as a network shared volume, then have the second machine backup over the network. This will only work while the first machine is powered on, so if you take it offset, the second machine won't back up.
> 3) which formatting protocol should I use?
Is this an SSD or a hard drive (My Passport comes in multiple varieties).
If it's a hard drive, MacOS Extended (Journaled) is the recommended format. For SSD, use APFS
> 4) Do I need to partition the EHD such that each laptop has its own section?
You don't have to. If you create multiple partitions, make sure that each machine is set to NOT backup the other drive's destination (for example, if you format the drive to "TM 1" and "TM 2" for machines 1 and 2, respectively, make sure that Machine 1 doesn't try to backup 'TM 2' as part of its normal backup routine (you can do this in Time Machine preferences).
> 5) Will each laptop be 'prompted' to backup to its own partition?
There is no prompting. When you setup Time Machine, you simply tell it what drive(s) to backup, and where to backup to. You can optionally tell it what NOT to backup. Once set, it's completely transparent.
