Is there some reason why it needs to be 10" specifically? 10" is a pretty uncommon size, and may needlessly limit your options to ancient netbooks from 15 years ago.
If something like a used 11-13" business laptop would be acceptable for your use case then there are a whole slew of options in the $50-70 range on ebay, maybe less if you find a good deal. I think there is also something to be said for getting something with a halfway reasonable keyboard which will not be agonizing to type on.
How so? I see plenty of posts by folks who recently switched from Windows, and I imagine the ones who are willing to take that leap in the first place lean towards the more tech-literate side.
"Willing to learn" is more subjective, perhaps, but I do not think my case is that uncommon.
I think that one's experience with Manjaro is often heavily dependent on how many AUR packages one has installed. Were you using many AUR packages?
Manjaro was my first distro for a year and it was fine. The occasional AUR dependency blockage was irritating for me but did not break anything.
My first distro was an Arch fork and I moved to vanilla Arch a year later. My problems in that time have been minimal. Personally, I am glad that someone recommended that I use an arch-based distro as a beginner. Mind you, I came in as a modestly computer-literate Windows refugee willing to learn. I think for those types of people it can be appropriate to recommend Arch-based distros.
So, yes, if you are not willing to google a problem, read a wiki, or use the terminal once in a while, Arch or its forks are probably not for you. I would probably not recommend Arch as a distro for someone's elderly grandparent or someone not comfortable with computers.
That said, I do not know that I agree with the assertion that Arch "breaks all the time," or that I even understand what "Arch bullshit®" is referring to. This overblown stereotype that Arch is some kind of mythical distro only a step removed from Linux From Scratch has to stop. None of that has been my experience for the last 4 years. Actually, if anything, it is the forks that get dependency issues (looking at you, Manjaro) and vanilla Arch has been really solid for me.
1). It matters a little bit, but not a ton. A big difference will come down to what package manager comes with a distro, and whether it is a "rolling" distro that gets updates as soon as they come out, or one which withholds updates until after they have some time for bug testing, etc. Given that gaming is one of your primary use cases, I would recommend a rolling distro. If your distro does not come prepackaged with something you can usually install it. Minimalist distros like Arch come with almost nothing pre-installed, not even a desktop environment, so you can be very granular about what gets installed and keep you system lean.
2). Most distros will not have as much in the way of corporate control/privacy concerns. A few like Ubuntu or Fedora are more closely linked with a single company, but most are more community driven and this is not a concern.
3). The advice I always give to people first trying Linux is to go into it with the mindset that you are learning a new skill, as many things are simply done differently to Windows. Most things work fine, but every once in a while, especially when setting something up for the first time, it may require additional configuration steps. Very popular distros like Mint will usually have the most community resources, and you can often find posts or guides of people who have already solved some issue you run into. I would also throw one of the Arch-based distros onto your list: Endeavour OS, which is essentially a pre-configured Arch installation. The Arch wiki is one of the most highly regarded resources in the entire linux community, and even if you are not using an Arch distro, many of the guides on it can be helpful.
4). Generally speaking, my multi-monitor usage with KDE has been seamless. No issues that I can think of. HDR support has only very recently been added, so I am not sure how well it works, but it is improving rapidly.
5). I think Plasma would be a good fit for what you are trying to do. Honestly, it is very customizable, but perfectly usable right out of the box even if you do not want to do anything to it. The layout is very familiar for a Windows user.
I think it is not possible to avoid it in all cases, but the reputation and business practices of the controlling company are your best indicator. Any changes to a company's culture may give signs if a piece of software may start to employ anti-consumer tactics.
Naturally, being closed source and in a dominant market position (i.e. a monopoly or near-monopoly) would make it easy for a company to start pulling these kinds of tactics. Sometimes even formerly reputable companies with open source software can try to do things like this after buyouts, changes in management, pressure from capital investors to increase profits, etc.
Generally, open source programs will be harder to monetize than closed source programs, as someone can fork the code and take out the disliked features. See Ungoogled chromium vs Google Chrome, VSCodium vs VSCode, Rocky Linux vs RHEL, etc.
Manjaro was my first distro. I used a number of AUR packages and ran into excessive dependency issues due to Manjaro's packages being held back and often a version or two behind. This eventually led me to switch to vanilla arch. Unless one plans on not using any AUR packages at all, I do not recommend it.
Manjaro also uses the pamac gui package manager, which has a bit of a history of "DDoS"-ing the AUR with excessive requests. Apparently, the search field in pamac would begin querying the AUR after every letter typed to try and populate autocomplete results, hammering it with requests. Pamac also does not distinguish between package repos, so even just having AUR enabled and searching for a regular repo package would send requests to the AUR. Apparently it got so bad that it took down the AUR and they started returning 403 to requests from pamac users. In fact, this happened a second time and got them blocked again. This got the Manjaro devs in bad graces with a number of Linux folks as it was not a bug, but a poor design choice.
Stick to the many guides available and you will be fine. One thing which I either missed or was glossed over in most guides is to install the Linux-firmware package. It is considered an "optional" package, but on all the machines I have ever used I have run into issues without it.
If it has an ethernet port (or perhaps a USB to ethernet dongle), maybe a PiHole DNS using Debian or the like? It is apparently supported on other Linux distros than Raspbian.
If it supports micro SD XC (i.e. capacities higher than 32GB) or you have a USB hard drive or high capacity USB flash drive, maybe a samba server for file storage? I often use my file server as a substitute for digging out a flash drive any time I want to quickly pass a file between two machines in my house.
Do you have the bolt and plasma-thunderbolt packages installed? I believe I had to do that to use a thunderbolt SSD enclosure/docks with my laptop. I am not sure about DP alt mode, though.
I think the voltage boosting microcode bug on 13th and 14th gen are generally considered to have been solved. I have not heard of any issues on the Intel 100/200 series CPUs. I would definitely recommend updating the BIOS on any 13th or 14th gen laptops, though.
I think an 11" laptop would probably be a better bet. Taking a quick look on Ebay, I am seeing things like Dell 3190s, 3180s and Lenovo Yoga 11e laptops for around $50 or so. I see some chromebooks with x86 processors for as little as $35, but I do not have much experience with installing Linux on chromebooks and so you may want to double-check how to do that before buying anything.