IMac 2008 vertical lines

This looks like a backlight uniformity issue.

This is where the screen isn't being evenly lit by the CCFL bulbs behind it. Some of them are outputting differing amounts of light and cause this perceived 'discolouration'. The lighter colours really do show it.

Unfortunately, this is one of the disadvantages of a CCFL backlight system as opposed to something like LED backlighting - backlight uniformity can become an issue, especially with time.

You'd be looking at a screen replacement - outside of warranty, that's gonna cost you.

Yes it is possible to diagnose and install macOS on an iMac with a broken LCD and missing hard drive.

The iMac all-in-ones from that vintage has a mini Display Port for a second display. It supports Leopard through El Capitan. Here’s what you’ll need at a minimum:

• A mini display port to VGA, DVI, or HDMI adapter, depending on the monitor you’re hooking up to.
• A bootable USB - either an installer or a USB with a full installation on it. You can create an installer by following one of the many guides found online. If you want to use the full install, you’ll need to install macOS to a USB flash (64GB is sufficient) or a USB hard drive.

As for a keyboard, I’m assuming it comes with one, but if it doesn’t, you don’t need an Apple one; a cheap USB keyboard will work fine. Just remember, the “Windows” and “Alt” keys are the Command and Option keys, respectively.