(1) Actually, it seems that pointing down is not currently supported. Sorry about that.
(2) Only hands, fingers, and pointables, not other objects. The Leap Motion Controller is designed for near-zero latency and high framerates, so it doesn't use point cloud or depth data, but instead returns input as frames. I highly recommend that you check out our developer documentation for more info.
(3) Glass can also interfere with tracking. However, many people have successfully tracked hands, fingers, and pointables through thin glass, placed against the device. Alan Davis, one of our engineers, has a great post in this thread about these sorts of setups.
(4) No, it cannot track a mouse.