What, you still here?!?! Sorry, just kidding.
This sure is unusual to be this difficult. And troubleshooting difficult problems can be long and tedious. Ruling out a bad download was important though... it is often a common source of trouble. I think we can safely assume that you have a solid USB installer though (but even that assumption is not a total 100%).
So, I am also assuming that you did just a basic install of Mint, entire disk, no encryption or LVM, and all that.
You call all of this "basically the same errors"... and you may be right. Each of your screen caps are different, but I agree that the core error is "kernel panic." Wikipedia
lists a few possible causes for kernel panic, so let's consider some... and what might we do to figure this out. (And hopefully Wizard or other smarter people jump in to help!
1. Any add-on hardware? This shouldn't mean your new SSD, but at least make sure there are no peripheral devices connected while you're working on this (no printers, scanners, any external devices, etc). This is not likely the problem, but there is some chance that Mint does not like your SSD and/or it wants an additional driver for it.
2. Malfunctioning RAM? This is actually a good possible suspect. My own belief is that most kernel panics are RAM related, though it might be an addressing problem and not necessarily RAM failure. At one point in your screen caps you could see an option for memtest86+ and this could help diagnose a problem with RAM. However, it takes a LONG time to complete, so you might start it up in the evening and let it run all night.
Another quicker RAM test, but not so thorough, is to open the compartment under your laptop and remove one of the chips (if you have two... I think you have 8GB, so I am hoping that it is 2 chips of 4GB each). Anyway, if there are two, remove the top one and try to boot the computer. If it runs well, maybe that chip is bad. If it still runs poorly, then swap the chips and try it again. If it runs well with each chip, but not both together, then swap switch one is in the bottom position... this could especially be true if different brand chips are used. Mint should really run fine with only 4GB if it seems that one of the chips is not performing properly. Be careful, but with a handle like @PcBuilderEd
I figure you know what you're doing.
3. Missing device driver? This might be tough to figure out. It kind of goes along with #1 (add-on hardware) and/or possible problems with RAM addressing. Anything particular weird or different about this laptop?
4. Unable to locate a root file system? Well, yeah... your newest screen cap was very specific on this one, so it is also a very likely suspect. But it's getting late, and I need to wrap this one up for tonight. A quick Google showed me these, but I have not read them all completely. But other people solving this problem means that you can probably solve it too.
Check this: https://ubuntuforums.org/showthread.php?t=2325051
(This was the shortest and quickest possibility. It is for Ubuntu, but Mint is based on Ubuntu so very possible to be the same. Of course you have an install USB to boot on instead of a DVD.)
Check this one carefully: https://ubuntuforums.org/showthread.php?t=1751574
(Try reading and see what you get out of this one.)
Check this one carefully too: https://forum.manjaro.org/t/kernel-...to-mount-root-fs-on-unknown-block-0-0/4620/10
(This is a different approach.)
5. Try another distro... perhaps this could be the least trouble to get you started with Linux. At least you could probably get something up and running more quickly without all the expert-level skills that you are acquiring!
Anyway, let us know which, if any, of these possible roads you wish to go down next, and we will try to help.