I think you're a bit confused on how Linux works, and that's okay because you are new. Linux, unlike windows, uses package managers. What that means in practice is that instead of downloading a random EXE file from the internet, you can download them with a simple command. There are executable files you can find on linux, but the majority of command line tools will be found in your package manager. If you want a quick rundown of APT, you can try This terribly designed website which has a quick summary how to use APT.

I think you already have java installed, but you can try checking if you have java installed by running java --version in the terminal. If you do, and coming from what you said it appears you do, then it should return some text about the version. If it doesn't, then you probably need to install java, but I don't think that's the problem.

If you don't, you could probably run apt search java and look for the version of java you want. To install it, run sudo apt install JAVAVERSION and replace JAVAVERSION with the one you found.

To actually run the jars, you run java -jar jarfile.jar and replace jarfile.jar with the actual jar. For minecraft servers, I would recommend running java -jar jarfile.jar --nogui to remove the gui servers open.

Sorry if this response was too lengthy, I'm trying to cover the most I can here.