Your opening statement is only partly correct:
As I understand, on the Commodore Amigas, the kickstart copies itself into a region of memory which is later made read-only.
This is true for the Amiga 1000 computer. The A1000 contains a small boot ROM which contains code to self-test and then request a Kickstart disk. Kickstart is loaded from disk into a special area of RAM called the Write Controlled Store, WCS. Then the boot ROM flips the WCS into read-only mode and reboots - this time the boot ROM is disabled and invisible, Kickstart is present where it needs to be in read-only memory, and Kickstart boots the machine. I asked a question about the A1000 WCS here which you might like to read to find out more details.
For all other Amigas, there is no boot ROM or WCS, and no Kickstart disk. Instead Kickstart is in a physical ROM - at power on, Kickstart is already in the right place in the memory map and, obviously for a ROM chip, is read-only.
(I understand that some Amiga 3000 models may be a special case - they have something called Superkickstart which can load Kickstart from somewhere else, but I do not know much more than that.)
Does kickstart also copy workbench into this region?
No, not exactly, but portions of "Workbench" are actually part of Kickstart.
If we are referring the the Workbench disk, then no - files on the disk are loaded into RAM and are lost whenever the Amiga is rebooted. They are not treated specially, and are not put into write-protected memory.
If we are referring to the Workbench "application": some of the Workbench app is on disk, but most of it is in Kickstart -
workbench.library contains the Workbench code. The
LoadWB command merely locates
workbench.library and tells it to start Workbench.
(In another special case, the Amiga 4000T ROMs, and the later 3.x ROMs from Cloanto, do not have
workbench.library in ROM, requiring that to be on disk instead. This is due to space constraints - space on the 512KiB ROM is at a premium, but it was relatively easy to shift
workbench.library onto disk and gain more space in the ROM. This is fine for hard drive based systems, but means that a lot of floppy disk apps suddenly become incompatible because they do not have workbench.library on disk.)
How does kickstart find workbench? It might be on a floppy; so is it stored in a particular location, like a MS-DOS boot floppy has a reserved region for booting?
Yes, this is correct - floppy disks have boot sectors. Kickstart loads the boot sector into RAM and executes it. On the Workbench disk - and many other disks - the boot sector contains a simple bit of code which simply calls back into Kickstart to say "yes, I'm a normal bootable disk, please boot me".
(Games and demos often had custom boot sectors which loaded the game/demo code directly; boot sector viruses had their own code to install themselves in memory and then called the "please boot me normally" Kickstart code so they behaved normally but hid their payload.)
Hard disks technically have boot blocks. I believe (but I am not certain) that these are actually unused, and when booting from hard disk Kickstart always goes straight to the "please boot me normally" routine instead of executing boot blocks.