Linux user for close to 30 years, here. Exclusively on linux since 2015 or thereabouts. I’ll give my tidbits on your linux-related questions, but I am no authority on this, as I’m a newbie on the subject:

1a - Is there no file system that works perfectly on both Linux and Windows? I could technically dual-boot using two different drives, but what if I need to access/move files between two drives with different file systems? Which issues would I face if, say, one is NTFS and the other is ext4? I think all of my drives are currently in NTFS, would I have to reformat everything to safely access them from Linux without worrying about data/metadata loss?

In general, Linux have good to great support for windows’ filesystems, NTFS included. The other way around is a bit more iffy - I remember that there was some sort of plugin/program that allowed me to mount an ext4 volume on Windows 7 eons ago, but I’m not sure how well it’s doing today. When I dualbooted, I solved this by using Windows as normal, and mounting the windows volume in linux.

1b - I read that to open an .exe on Linux I would have to do it through WINE, and that there’s a database to check compatibility of individual programs with it, but are the worst compatibility issues just “the program doesn’t open”, or can a compatibility issue result in data loss/corruption too?

Compatibility with windows software is very forgiving. It doesn’t really cause any corruption in the sense that a windows program won’t go amok on your linux installation and start wrecking stuff because it’s not incompatible. It’s more a matter of it failing to start properly, or doesn’t work the way it should.
However, this isn’t as complicated as it might seem. Many games, for example, run fine via Proton in Steam, and this is more or less a transparent process in that you don’t have to do anything special.
And it’s worth noting that most windows software has a native linux alternative. I suggest you do some research into specific programs you need, and see if there’s a linux release for it, or if there’s a viable alternative for you.

1c - I’m currently using Firefox on Windows, is it possible to copy all my settings and data (browsing history included) from the Windows version to the Linux one?
I honestly don’t know. Firefox has been advertising its sync feature to me for ages, but I never bothered with checking it out.

1d - Other than specific .exe without WINE compatibility, are there any relatively common file types which can’t be opened with Linux that I should be aware of? (Mostly talking about picture/video/audio/text files, compressed archives or similar). No. A file is in itself not a limitation. Only the programs used to read and interpret them are. I have not found a common file type that doesn’t have a linux native program for reading it.

1e - What can I mess up by testing an USB live version? Are there any things I should be careful about? I’ve heard “changes aren’t saved”, but that’s referring only to OS configuration, right? And, going back to file systems, can I even access the data that’s on my NTFS drive from a live version or would I just be working with the stuff inside the USB? A live USB version doesn’t affect your system (under normal circumstances). It reads everything it needs from the USB, and if you install software, it is only installed in memory and not on your harddrive or USB stick. It is possible to mount your existing filesystems and access your persistent storage that way, but you will only affect it in whatever manner you chose to. So in other words, if you boot from a live USB, you have to actually try to ruin anything on your disk - I’m having a hard time imagining how one would do this by accident.

1f - I read often that “you can’t get viruses on Linux”, but that’s mostly because they’re not developed specifically for it, so you might “get” them but they won’t work, right? If I dual boot, is there the chance that I get a malware while browsing with Linux and then it infects my pc when I boot Windows (even without consciously opening unknown .exe files)?
In theory it’s possible, but in practice it doesn’t happen. A virus targeting linux for people who dualboot is a very narrow target area, so I wouldn’t worry about it.

1g - Which Pc components should I pay attention to because they/their drivers might not work on Linux? Is there a site/tool that can check if my current hardware would have any issues? (For example, I have a Nvidia graphics card and I think I read that might be a problem?) Hardware compatibility isn’t much of an issue that anymore. I see a lot of people complaining about NVIDIA drivers on linux, but I never had any issues myself. I run a fairly stock Linux Mint 22.1, and everything worked out of the box. On my previous install, when the laptop was brand new, I had to update the kernel so that I could install an NVIDIA driver new enough to handle my GPU, but it wasn’t much of an issue.
It is worth noting that hardware compatibility often comes down to your choice of distro. While all distros are technically compatible, some distros are more focused on “It should just work out of the box” and that’s why I prefer Mint as a desktop OS.