GPS receivers download an almanac from the satellites, in order to know what satellites to look for. If you turn your GPS off and move it a few thousand miles, it has no idea you did that, and will look for the satellites it thinks will be overhead at that time. If it doesn't find them, then it has to start a new search, and find out what satellites are in view. The GPS satellites are not in geosynchronous orbits, but in polar orbits, moving from north to south, covering different areas as the earth spins below them. It can take up to half an hour for the GPS to find itself, although newer chipsets should find a position more quickly. On standalone models you can usually tell it to start a new search, which is quicker than continuing to search based on the last known location. If you move the GPS from the US to China, don't expect to get an immediate lock, it will take time even with a clear view of the sky. Other than that, there is nothing special about China. GPS is designed to work anywhere on the surface of the earth, thus the GLOBAL in the name.

Metal and water will block the GPS signals completely. The water in you hand is more than enough to block the signals, and the metal fuselage of an airliner will also block them. You can usually get a signal at a window, but it won't let you see all the satellites overhead, just the ones in the direction of the window.

Whether the GPS will work at airliner speeds depends on the manufacturer. They can prevent it from working at whatever speeds or altitudes they want, or not. There is no technical reason they can't work at any altitude or speed, other than the US government not wanting them to.

GPS receivers, bluetooth or not, won't affect aircraft navigation instruments. Neither will laptops or much of anything else. The reason for any prohibition is that the FAA, in its infinite wisdom, requires any airline (or any other commercial aircraft operator) to prohibit all electronic devices unless that operator has tested the specific devices, or types of device, and determined that they don't interfere with the avionics. Some airlines care about their customers and do the tests,which are minimal, and some don't. I've personally tested many devices, and have never found one which caused a problem. I used my own personal GPS mounted to the instrument panel for a long time before GPS was installed in our aircraft, and if it won't cause a problem there, it won't cause one from back in the passenger area. Many airliners still don't have GPS installed, because it really isn't necessary. Flying between major airports doesn't require GPS at all, but flying to other places can.