There’s pros and cons. On one hand, packing your dependencies into your executable leads to never having to worry about broken dependencies, but also leads you into other problems. What happens when a dependency has a security update? Now you need an updated executable for every executable that has that bundled dependency. What if the developer has stopped maintaining it and the code is closed source? Well, you are out of luck. You either have the vulnerability or you stop using the program. Additionally bundling dependencies can drastically increase executable size. This is partially why C programs are so small, because they can rely on glibc when not all languages have such a core ubiquitous library.
As an aside, if you do prefer the bundled dependency approach, it is actually available on Linux. For example, you can use appimages, which are very similar to a portable exe file on windows. Of course, you may run afoul of the previously mentioned issues, but it may be an option depending on what was released.
Sure. If you are using an nvidia optimus laptop, you should also add __NV_PRIME_RENDER_OFFLOAD=1 __GLX_VENDOR_LIBRARY_NAME=nvidia at the start of the last line when running in hybrid mode to run mpv on the dgpu. You should have a file at ~/.wallpaperrc that contains wallpaper_playlist: /path/to/mpv/playlist. You may want to add this script to your startup sequence via your wm/de.
I set mpv as the root window which worked well. I stopped using it a while back, but if you are interested, I could dig up the simple script for you (literally one or two lines iirc).
pass would meet your requirements. It is a super simple implementation of a password manager levying PGP for encryption and git for syncing. You can therefore use any git server for syncing. There are browser extensions for autofill etc and scripts to import/export passwords etc.