Yes, as long as your Laptop has an HDMI output, or you use an HDMI adaptor, you can enjoy the large screen experience with Skylarx.
If your Projector / Beamer has a HDMI input, then yes you can use your Skylarx together with this source.
Yes, Skylarx is compatible with all Set Top Boxes as long as they have an HDMI output.
No, the two units need to be in the same room with a clear line of sight (up to 30 metres distance). The units will not work through walls.
The green HDMI cable needs to be connected to the Transmitter which has a green HDMI socket. The red HDMI cable needs to be connected to the Receiver which has a red HDMI socket.