It sounds like you need an introduction to git! There are a lot of good tutorials/how-to-learn on git, here are a couple of my favouite, especially for beginners.
http://pcottle.github.io/learnGitBranching/
But, to answer your questions:
1) No, you must create a repo first, and then you can add files to the repo. The best way to go about this is create a repo, clone it, move files into that folder, commit the files, then push them. There is a way to initialize a git repo inside of an existing directory, but it's sort of a hassle to do it that way (a bit more complex). Cloning and moving will simplify things.
2) You need to commit to your changes before you push them! After you make a change, it isn't actually logged as being changed until you commit them to history (and the history is what determines what gets pushed to the repo)
3) I'd move the contents of your project folders into your cloned git repo, commit and push that.