To me, your question looks extremely broad, making it almost impossible to answer. It's covers many topics and many of them are very wide by themself and/or doesn't have a single answer. For example, we can spend of lot of time discuss possible branching strategies for Git, but there is no single best one you should use. Also, this topic is already covered at other places, so maybe we shouldn't even try to duplicate it here.
It would be better if you don't try to cover everything at once. I suggest you split it to smaller thread and ask more specific questions. When you say something like "initial repository setup", it's not really clear what you need from us. Does it mean that you don't how to create a git repository at all? Or does it mean that you have a problem specific to F&O, but you didn't explain what it is?
In general, you need to decide where you'll host your Git repository. If you want to use GitHub actions, you'll probably want to use GitHub, but it's not strictly necessary. How to create a repository then depends on the hosting system (GitGub, Azure DevOps...), therefore you must make the decision first.
Regarding GitHub actions, I'm not aware of any resources covering GitHub Actions for F&O. You've decided to use that, so it's up to you to develop it. But you don't have to start from scratch. There are examples of build and release pipelines for Azure DevOps, which will help you when building your GitHub actions. Often the actual job is done by .exe or .ps1 files executed by pipelines and you'll be able to do the same in GitHub actions.
I'm not aware of any dependency of package deployment on TFVC. A source control system is involved when getting code for a deployable package, but the deployable package is the same regardless of where the code was located, and the package isn't stored in source control. You deploy the file to LCS.