As for what is part of what, anything you do with the ‘git’ command is part of git. Anything you have to do on github.com is not.
Just to be clear we can create a branch on github as well as on git though I am not forced to do so on github. This maybe confusing for a beginner as both provide branching.
PRs are native to GitHub, but I can send you an email Requesting that you Pull from my remote. The Linux kernel team still emails patches I think.
Issues are a GitHub thing.
There are plenty of other alternatives, including ones you can host yourself, the most popular that I've seen being GitLab and BitBucket.
"GitHub" is essentially just "git" on some someone else's computer with a bunch of extra features.
The comment below you answered my question : PR/Issues are native to github.
https://www.gerritcodereview.com/
Incidentally Gerrit predates github.
I understand from your comment that it's not your preference but that doesn't mean its not a self hosted git solution.
The problem with submitting a rebased branch is that while there are no apparent merge conflict and your changes appear to have been developed on the tip of master, your changes may actually have been developed on a much older version of master. Builds may appear to compile fine but they might not make sense - when you discard and rebase the context of commits, you lose important information.