I think on mutable distros, or at least arch, you can run a command to reinstall all installed packages, which will verify integrity of the package files (signatures) and then ensure the files in the filesystem match package files? And I think it takes minutes at most, at least for typical setups.
I do think it’s also possible to just verify integrity of all files installed from a package, but I don’t remember if it required an external utility, pretty sure it’s on the arch wiki under pacman/tips and tricks
There’s nothing special about it. Linux distros are one of the options, alongside windows and osx as desktop systems.
What there are are preferences, morals, affordability. Linux is generally free, has different approaches to how the system is structured, how software is installed, how much access to the system you have, and how much responsibility for setting it up you have.
This will also vary from distro to distro, but generally software is installed from the distribution’s repositories, not downloading files from various websites - and instead of having some different scheme for updating every program on your computer, you use a single command (or button in an app) to update your system and all your software. This is one of the main things I love about Linux - you get to update your stuff when you want, all at once.