What is the correct way to make the remote branches/tags that exist after a git-svn init/git-svn fetch into local Git branches/tags before pushing to my remote Git repo and
To do exactly that you want just use SubGit project. You can install it into your SVN repository. So that a linked Git repository is created (with SVN tags translated to Git tags, svn:ignores to .gitignore and so on). That Git repository is kept in sync with the SVN repository: when you push to a Git repository, this changes is translated to the SVN repository, and vice versa.
If you need client-only solution, I would recommend you to use SmartGit. It also preserves SVN concepts in Git repository.
And what I wouldn't recommend you to use it git-svn.