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I will repeat information you already know here in case anyone in Rio Linda wants to follow along.
I made lists of programs for which I wanted a clean download and went to the library to use their computers. I like the way the library computers allow me to download to a hard drive and copy to my flash, and when I log off and log back in, the OS has 'forgotten' I was there previously.
I wondered how the library does that - what software they might use. I noted their system uses 'Cybrarian'. The library computer takes long enough to reboot after I log off for me to guess that it is reinstalling an image to at least one partition (user files) and possibly more (browser add ons?)
The library uses 'Cybrarian' to run the library guest computers. I was going to look into it, to see if it automates re-installatin of partitions or if it is only to grant users access, techs remote control for maintenance etc. When I returned home, I searched for the program and noticed that although the search results below look, at first glance, legitimate, the second listing uses a different spelling in their domain name. I have to say I'm skeptical that the second site is legit.
This puts a cherry on top of the 2 hours I spent in the library trying, and failing to find a way to download a clean version of any file.
I tried installing NoScript (thank you for the recommendation(s)) and it was easily done. I blocked google but while working google search results emerged. I hadn't reasoned that the declared search engine in settings could over ride NoScript settings because Settings in Firefox are not scripts. *face palm*
Since I saw scripts pouncing on every attempt to load websites like rufus.com, I searched to find the download page and wrote down the full URL (I was optimistic).
I switched the browser Search setting to 'Bing.' I didn't see any ride-alongs when I navigated to Bing.com.
So I rebooted and installed noscript in the firefox browser again - turning off everything in the NoScript 'settings' list.
I went to Bing.com (all was well) but when I tried to follow search results off the Bing page, I kept experiencing thread hi-jack (the first 3 letter prefix of the very very long link was 'ink'). The library's security software advised me the page I was trying to access had a different URL and was an ad server. That happened regardless of which website I followed (rufus etc.), so I still couldn't download my files. Well, let's say I didn't feel comfortable doing so.
I tested DuckDuckGo primary website and didn't see any scripts running. But I didn't have time to test if I can actually try downloading rufus without thread hijacking.
I was there to download Windows64 from microsoft - which almost worked but my guest permission limits block running the installation software needed to save the Windows65 ISO, so even if DuckDuckGo works, I can't get a clean install for Windows there.
A friend is happy to loan me his flash drive Windows install media, but he has elected to live with malware in the belief that there's no escape, so I don't see how his flash drive could be 'clean'.
Quesion 1:
I know I created a recovery flash there weeks ago, but no doubt it was permeated by Google before I got there. If Microsoft erases everything on a recovery flash drive before installing recovery software, is there any hope that malware was not also installed on the recovery flash?
Question 2: Is there any hope of finding, if there is a recovery partition on my computer, that the recovery software is not now 'owned and operated' by malware? By that I mean, could a recovery partion still supply a clean, outdated copy of Windows?
Question 3: I downloaded linux and created an installation USB. Since the hash was valid, then I could have transfered other kinds of problems to my computer, but the Linux ISO is still valid, right?
4. If the answer to Question 3 is 'yes', then might the same hold true if I hvae a compromised machine, download Windows64 to create an ISO, and if there's a valid hash of that file, the file MIGHT still be able to create an CLEAN USB install copy of Windows? Malware present but not on the flash (my fingers are crossed here).
5. I used to think purchasing a copy of the disc from Microsoft would mean a clean install, but I am jaded. But still, is it the cleanest way to install Windows10 in this day and age? Still, buying a disc when the program is free would be a poke in the eye, but perhaps it's the only way?
6. Should I give up, install Linux 'along side' my computer's Mad Max version of Windows64, and never launch the internet from the windows partition, or just surf the web but no downloading? *sigh*
My preference is create a clean install of WIndows64 (make an image) and then load my programs on top of it (make a second image here) and then figure out how to 'lock down' my machine the way the library does it? Meanwhile, try to learn to transition to linux.

If the hash was good on the Linux then it is clean. It is exactly as it is meant to be without any adulteration or the hash would be fouled. In fact if you boot into that Linux USB there will also be a momentary menu with an option to “check the integrity” of the complete download. If there are any issues it will give you a warning with details.

From experience and a lot of years using it, the Rufus is safe.

“5. I used to think purchasing a copy of the disc from Microsoft would mean a clean install, but I am jaded. But still, is it the cleanest way to install Windows10 in this day and age? Still, buying a disc when the program is free would be a poke in the eye, but perhaps it’s the only way?”

Unfortunately that is the only way to make sure a third party has not added their own stuff. It should come with a warranty and a license which makes it relatively trustworthy.