Can you take a laptop with you when you're sitting in the plane or using it?
Yes you may.
Yes. May one. Only at take-off and landing, the laptops, cell phones etc. Have to be off
Yes,
Yes, as long as you do not use a transmitter / receiver that CAN affect the aircraft systems (see EU-OPS 1.110 - "Portable electronic devices"); unless the plane is already converted for the Internet, if you speculate on it.