One of the strong suits of USB is the downward compatibility. So it should work. But check the description of your enclosure.
You can run a 990 Pro without a heatsink but be prepared for thermal throttling when you use the drive a bit more. TBH getting a 4.0 case is kinda pointless without a heatsink
Option 1 does work but laptops are not ideal as a server. They lack the IO and have tiny heatsinks that tend to get clogged with dust. And those USB DAS are kinda expensive. And USB is less reliable than SATA although it usually works well enough for something non critical like a media server.
Option 2 is kinda bad as this NAS is too low end to run Plex. You need something with an Intel CPU.
You can get a used desktop PC for $1-200 that has a 6th Gen Intel 4 core CPU or newer and is able to house 4 drives or more. Only needs a bit more of power than option 1 or 2 but is cheap and works rather well as a NAS and server.
Automating and streaming backups is definitely the way to go. Otherwise, it is really likely your backups are outdated and/or incomplete.
Please add the capacity of your drives. Upgrading to fewer, high capacity drives can be well worth it.
Build a NAS with 100TB and then start downloading. 90TB should take about 10 bays to download with a 1Gbit line. Although your ISP might get mad.
Backups and even accessing files can be a bit of a pain with two OS. NTFS drivers for Linux are a thing and they mostly work but I would not overly rely on it. For this reason, I would consider using a NAS for storing and accessing your files. It can also handle your backups with Rclone.
Data recovery is not really something you should DIY unless you are fine with losing the data. Chances are high you will make professional recovery more expensive or outright impossible by tinkering yourself.
Your best bet is to make a disk image. For this the HDD will be read like a vinyl record from beginning to end. For a file copy the read head usually has to seek around a lot to read all the file (fragments) bit by bit.
10TB for €120? Are these used drives?
I would strongly consider bigger drives. 18TB or more. Using small drives is expensive in the long run. More W per TB, more bays per TB, need for bigger and more expensive cases, need for HBAs and maybe some high end platform to get enough PCIe lanes etc.
i5 processor
What i5? If it has an iGPU you most likely should remove the 970. Will just needless eat power and PCIe lanes in this setup.
setup both hard drives as a raid 1
You mean RAIDz1?
I would consider something else than TrueNAS and ZFS as a home user. It is a robust OS and file system but usually not the best option for most small home setups. mergerFS+Snapraid or Unraid are far more flexible as they allow you to add single drives of any size down the line. The performance and reliability are usually good enough for a home user with a 1, or 2.5Gbe network.
Once your system is setup tinker a bit with the OS, setup some file shares and once you know how to set up everything properly copy your stuff over and verify afterward if it was done correctly. Not really a big deal.
Not a bad idea although you can move files even while the drive is still part of your merge. Although this can put some extra strain on it.
If you want to be as gentle as possible a full drive image is usually your best option unless the drive is mostly empthy.
Just wanted to mention this as well. Newegg tends to package HDDs poorly. So be prepared to receive damaged drives.
USB is even cheaper and far easier to find these days.
Snapraid is only for parity. If you intend to pool up your storage you need something else like mergerFS on top of it. But if you care about performance it is not really a great option.
"Best" is usually a vague term. Best would be likely a high end enterprise SSD. Costs about as much as a car but is reliable and pumps out data at multi GB/s speed all day long.
How much storage do you need?
How big is your budget?
How fast does it have to be?
How large are your games usually?