I'm not sure what "Flymod" is. Do you mean looking around with WASD and the mouse, kinda like the original FPS speculating views?
In Godot 3 you can press right mouse in the main view and use the WASD keys to move around the scene. In Godot 2 and 3 you can drag the screen by pressing shift and middle mouse button and rotate with the middle mouse button (as you found out)
You can save Scene tab (in Godot 2) and hitting the save button. You can also save by pressing Control-S, and that will save the current scene. There is no need to save a project in Godot, just the scenes that make it up.
Also, when you can set the main scene in the project settings, which you can find under the Scene tab in Godot 2 and Project tab in Godot 3.
Hopefully that answers your questions. Let me know if you have any issues and I'll try to help.
