This is a context menu that contains menu items that can operate on the selected files. Stash does not operate on selected files, but always on the whole repository. Hence I voted against this request.

Mark your repository as favorite. This will automatically fetch the latest changes.

The Output window is just that: the output display. If you want to use a command line, you can open one from the repository's context menu.

Maybe you misunderstood. In the SmartGit preferences you can configure the sync-order - either push, then pull or pull, then push.

Have you tried SmartGit 8 preview?