How much storage do I need in a partition for a startup external hard drive ?

Yes, if the drive is large enough to have three partitions, then you could install two different OS versions with a third volume for other storage needs (not backups.) The size of the OS partitions should be determined by how much you want for each OS in terms of non-OS files such as third-party apps and such. Catalina requires more space than El Capitan for the OS. Of course, the computer must be bootable from either OS. If this external drive is a HDD then format using HFS+. If it's an SSD to format the El Capitan partition HFS+ and the Catalina partition with APFS. You can only do that using Catalina.

Depends. If you are creating a bootable USB macOS installer, then you need 8GBs except for Catalina which requires 16GBs. If you wish to install a whole system as an alternative startup volume, then you need a minimum of around 30GBs. This will vary depending upon how much RAM is installed and how much third-party software you install. If you want to clone your existing system, then you need at least the capacity of the source volume.

What I posted before applies to El Capitan. Is that the version you want to install on the external drive? Do you have an El Capitan full installer? If so, then you want to make a bootable USB flash drive installer from the El Capitan application. Before you do the installation you will need to create the partition on the external drive. Is the external drive currently empty or do you already have files on it? Do you know how to create the partition? What version of macOS are you currently running?