Sounds like the DVD may be dirty or just not readable.
If the lens on the drive is a bit dusty, it will read some disks and not others as well.
Yes, it is a good idea to remove all drives except the one you are installing to.
Then when you add the drives back again, start with what was the D drive and make sure it is the D drive after putting it back, and change the drive letter if it is not what you want it to be before putting the next drive back.
Other things you may want to back up are the favourites folder (most browsers now you have to export and import) the fonts folder, and any add-ons or plug ins that may be in the programmes folder, unless you have them elsewhere. I never store emails only locally, I always leave copies on the mail server, deleting them from the server was an old idea when data was limited or expensive, but if you have deleted them from the server, emails will need to be backed up, if they are on the server you will be able to download them all again.
I always use an account with admin rights, but by default it still asks for permission to make any system changes.
You can't just copy a DVD to a USB stick if you want it to boot, however the software asks you whether you want to create a DVD or USB boot device.
It is important during the first stages of install to delete all the old partitions and let the install create them again.
If you bought w10 pro on DVD then I think that is the best thing to use, as the key will be correct for it. You cold not use your key to install from a volume licence edition DVD, not could you use a volume licence key to install from your DVD. The licence key will determine many things such as what features are installed etc, not just that you have a licence. That means the installation will probably be common, and what you get depends on your key. I have never installed home edition, so can't say that from experience.
If it was mine, I would remove all drives except the system drive and the DVD drive. I would remove the graphics card too, and any other hardware extras.
Reset the BIOS to default, check that it sees the system drive (you may have to change the settings for it to see the drive, and you may have to change them later for the installation to run correctly, but usually not)
Run a fresh install from the purchased DVD, deleting all partitions, complete the install, then run updates as many times as it takes until it says none available.
Install what ever programmes you want on the system drive. (I install all programmes on the system drive, they will often not run from another drive without reinstalling anyway, as all the registry entries for those programmes will be missing)
Run it for a while, enter the key etc and make sure it is accepted for a few days, install Malwarebytes and SyncFolder app from microsoft (the easiest and quickest way to make backups I have found)
Add your data drive, and back it up.
If all is well, put the video card back in and install the drivers it needs.
I personally think all will be well
Couple of random thoughts, having done similar every day for 25 odd years before I stopped work, it is a bit different doing it, where your instincts and past experiences tend to put you on autopilot, than it is trying to think of the processes to write down. I know that others doing it for a living find the same thing, some may not.
Also, you referred back to posts where you had already answered something, or had already been said. Unfortunately that is a feature of threads like this, simply if people had to keep up to date with the thread, they would not reply
Also, you will get the same thing said in different was from different people
You said you have two M2 drives, have you already put data on the second one? If not, or if you have it securely backed up, it might be an idea to use that as the new system drive, incase you don't save something you need from the old one, though as it was cloned, I would assume you still have the source drive?
With windows, re-installing is not a nuclear option, it is a basic one