Just use an aux cord.
I still use a 2007 20” Cinema Display every day. It works fine for basic stuff. Maybe look for a cheap one on the market, but you might need a DVI adapter.
For data transfer, USB would be slower but easier. There’s also an Apple FireWire to Thunderbolt 2 adapter, then a Thunderbolt 2 to Thunderbolt 3 adapter.
You’ll need a FireWire 800 cable and a FireWire 800 to Thunderbolt adapter, then a Thunderbolt to USB-C adapter. Start the iMac in Target Disk Mode by holding down the T key. I’ve linked the parts below.
What year is your iMac? You can check under the Apple logo in ‘About This Mac.’
No need for cables. Use SMB over Wi-Fi to share files.
What exactly are you trying to do? Also, it looks like there’s something stuck in your Ethernet port.