I use electron to create cross-platform application. For Windows and Mac it could be done by electron tools, like autoUpdate, Squirrel, so on.
The problem is only with Linux. I have built a .deb package for Ubuntu. But I can't find any "step-by-step" instruction or comprehensive info about it.
I'm not familiar with java and hadn't experience with creating apps for Linux.
So the main questions are:
There really is nothing standard in the *nix world. You will always have to support specific ditributions, and each of these distribution can in turn have multiple possible ways of creating an auto-updater.
To your questions:
There is no standard way.
That depends on your way of actually distributing he package. If you plan on using package managers like rpm/apt-get/apt install, then each of these managers has a specific way of configuring your application to be among those packages that are checked for automatic updates.
Difference between .rpm / .deb:
Main difference for a package maintainer (I think that would be 'developer' in Debian lingo) is the way package meta-data and accompanying scripts come together. Link
Difference between Ubuntu & Fedora: As creating a detailed answer on this questions would both be too lengthy and too much effort to maintain, check out this blog post detailing the differences between these two distributions.