Popup should be shown right after action is performed (or before it is performed) but after user clicked on menu item. For example in Eclipse IDE you can enable/disable this feature. You have two options: a) when action is invoked via keyboard b) when action is invoked via mouse click. I think 'a' is not about showing popup when you used F7 to create a branch its about using Alt+B to open Branch menu item and then use arrows to navigate down and press Enter on the menu item (e.g. you invoke command using keyboard bot not by using hotkey shortcuts).

Way you say "already show the shortcut" you most likely mean that menu items have name and shortcut displayed in the menu item. My point is about showing a popup when you click on menu item and this way 'teach' user about most common shortcuts. Added picture how it looks like in Eclipse IDE

No my suggestion is not about non-pushed commits. Its about showing what were recently added to the history after pull or rebase. So if highlighted in different color it is easy to go through and check each one.

Well I suggest add two options for user and let him choose what he want. Options are:
- Enhance "Search for Repositories" currently it finds all repositories in particular folder and them to list of repositories. But this structure is flat while directory may contain nested projects with similar names like: <selected folder>\nested-project-a\nested-project-b and <selected folder>\nested-project-c\nested-project-b. Not sure if it will be able to add both cause they have same name. Instead allow it to import projects while preserving hierarchy. So non git-repository folders will be navigable as git repositories but they will have less actions available (cause they do not need some actions like commit, pull etc). I understand that currently adding folders is not supported but at least you can let user choose option: "import as groups" and create groups automatically based on folder structure. For each folder which is not an git repository create group and move add nested git repositories to it. For nested folders create nested group and so on.
- More advanced alternative partially described in previous option: allow adding directories not only git repositories. Currently if you are trying add folder it enforces you to initialize it as git repository. So basically you can change existing dialog "Repository > Add or Create" than "Select directory", "OK". It shows another dialog "Add or Create repository" with two options: "Initialize" and "Cancel". You can add 3rd option: "Open as folder" and show it in the list of repositories as like regular repository but with difference set of allowed actions

From my point of view nothing should stop developers from adding this feature, since anyone who don't like it would use first nested level.
Another key point: it may be very useful when organization is huge and there are a lot of different teams working on set projects, so you can reflect that in group hierarchy. However this can be done in other way: by using tags for git projects instead of group hierarchy