2011 iMAC Catalina external bootable drive

I take it you no longer have the optical system install/restore disks that came with the computer?

Do you have access to another computer to use for downloads?

This article is about making a bootable USB installer:

How to create a bootable installer for macOS - Apple Support

A High Sierra link is in that article. Be sure to note that the media must be formatted for Mac:

A USB flash drive or other secondary volume formatted as Mac OS Extended, with at least 14GB of available storage

WAP4444 wrote:

I do not need to create an installer USB drive.

I need to create a High Sierra bootable USB drive, which i can then use to boot my iMac from, and hopefully recover files from my HD.

I do not need to create an installer drive...unless that will allow me to also do the recovery.

Yes you need to create a bootable macOS USB installer so you can actually install macOS onto another USB drive unless of course you can boot into local Recovery Mode using Command + R (unlikely with a failing hard drive) or Internet Recovery Mode using Command + Option + R (unlikely since you are running macOS 10.11, although Apple's documentation is a bit confusing on this point).

If you know how to use the command line, then you can also use the macOS USB installer to transfer your files to external media, but this is not something we can easily help with since using the command line is very difficult and it is extremely easy to make a horrific mistake even if you know how to use the command line and have years of experience.

FYI, you should always have frequent and regular backups for situations just like this and for the times when you may accidentally modify or delete an important file(s).

You can use your internal HD Recovery Partition to format and install Mac OS (up to 10.13.6) to an external HD. The quickest you will find is a Firewire 800 which is very slow by today's standards. Something like:

https://eshop.macsales.com/shop/firewire/1394/USB/EliteAL/eSATA_FW800_FW400_USB

would be your best bet.

However if you want to clone your internal HD to the external use an app such as SuperDuper! or Carbon Copy Cloner. Simpy clone from the internal HD to the external HD and then boot from the external HD. Finally just set the external HD as your boot drive.

That's not possible without using unsupported hacks to get it on your machine.

The 2011 iMac can not run anything higher than High Sierra.

One would think that if you're savvy enough to hack an unsupported OS onto your Mac, you would be able to figure out how to create a bootable drive...

Why don't you explain what's actually going on?