Can I copy a bootable El Capitan installer USB stick to a hard drive partition and install from there?
No, you can't just copy the files from one to another drive and assume that the new drive will install El Capitan. There is a special command to create such an install drive, called createinstallmedia which runs in Terminal


Download the OS X installer from the Mac App Store. Quit the installer if it opens automatically after downloading. The installer will be in your Applications folder.
Mount your USB flash drive or other volume. You could also use a secondary internal partition.
Open the Terminal app, which is in the Utilities folder of your Applications folder.
Use the createinstallmedia command in Terminal to create the bootable installer. 


If you're creating from an existing El Capitan machine, please use the following command. 

sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app


I haven't personally tried doing this with an external hard drive instead of a thumb drive. But I don't see any reason for it not to work. 

For more details and how to configure the above command (it depends on the OS you're installing to the USB drive from), please refer to https://support.apple.com/en-gb/HT201372