I believe it has those options on the camera's main page under the direction arrows marked "flip", "mirror". To be sure it works exactly as you need the user manuals to foscam cameras are online and provide images and examples.
Yes, it does. You have mirror and flip options available for doing just that. You will see them when logged in and operating the camera from your computer. They are just under the directional pad for panning and tilting the camera.
The software has a "mirror" and a "flip" option for the image and the unit comes with a nice mount to be used on a wall or ceiling. Although I have not tried it, I would say yes but the pan/tilt I have experimented with on the camera would suggest that it can only look straight up (or down ) if on the ceiling and then forward from there so a slight tilt of the mounting bracket or mounting the camera on the ceiling, near a back wall might be in order... I think you can easily make it work however.
It does include both flip and mirror options, but it would be difficult to mount flush to the ceiling (as there is only one screw hole on the bottom of the camera base). It does, however, come with a ceiling/wall/anything mount and hardware to attach to drywall.