• I'd strongly advise you to stay clear of elementaryOS, at least as a first step. after you figure things out with a more vanilla flavor, feel free to revisit it. there's enough challenges with taming that hardware with vanilla flavors, you don't need additional ones
• these aren't important messages, if you want to look at what's happening, press "e" on the GRUB menu and remove quiet from the switches edit: those are EFI messages, that's not linux stuff. make sure your USB drive is GPT formatted and after you've flashed it verify there's an efi folder on it. reboot, press and hold Alt until the menu shows.
• you're booting with Nvidia graphics. those are abject horror in the best of cases, and yours (GT330M) is beyond saving. you should disable it as you'll get nothing but grief and run it on Intel HD graphics only, here's a primer.

What I've learned from installing Arch on a 2007 (I think) MacBook is that Apple uses (or used) some mangled EFI implementation that doesn't always jive with standard bootable devices.
I had to install rEFIt to get the Arch stick to boot. Nowadays rEFInd may also be a good fit.

Try SMC / PRAM Reset?

With references to APFS and fusion, it seems like it might be trying to mount a visible filesystem.

If the intention is OS install, try erasing the disk from recovery mode and formatting as something ‘boring’ like ExFAT

No expert but an uuid with a bunch of zeros seems really odd to me - and if I'm guessing correctly, boot is failing to mount your partitions as if the filesystems were corrupt, but I'm just leaving this as bait as someone with more knowledge about that stuff corrects me. In the meanwhile I'd check things to really be sure the hdd drive is ok (via fsck, parted and co)

maybe try another distro or rescue live image to make sure it's not about missing specific drivers in that particular installation iso?

I recall trying to install Linux on a 2007 Macbook and several distros not working. I guess try a different distro. I don't know why some work and some don't but I'm just gonna blame Apple. Try Fedora or endeavourOS. I even found this script to install Elementary's Pantheon DE on Arch Linux.

Edit: Also Debian might be worth a try.

The most recent release often gave me problems. Get the next one back until they clean some things up. Also I have been using Impression to write my flash drives. Give it a try.