1) As much as possible. If possible, nothing should be to the side of the device for as many mm as possible
2) This depends on the antenna used and its radiation pattern (where the lobes are). You want to interfere as little as possible with these lobes
3) Any metal should be kept out. Copper traces could make things worse since it would cause noise and might fail FCC certification.
The reality in the answers is this. Give as much clearance as you can and most of all follow the manufacturer rules. If a certain product can only give 5mm of clearance, then it is what it is. It will affect the radiation pattern, but how much is difficult to tell unless complex simulations or an anaechoic chamber is used.
As a point of reference look at the small USB transceivers sold with Wireless Mice. The transceiver is inside the actual USB connector, with only the antenna sticking out. For marketing/design purposes, they kept it very short and they typically get away with it, although the range isn't the best. But, for their application where the mouse is only a few feet away it is good.
I've done a few products with very tight routing and antenna location. When things got very bad and the effects of the metal surrounding the antenna or routing cause packets to drop, the solution was to move the antenna. Basically use a U.FL connector or similar with a small 50 ohm cable (these are specially built) and place the antenna in another location, or have a custom antenna made that can give you the radiation pattern you desire.
So, in the end the design depends on many other factors. You don't always get the luxury of the perfect keepout area.
In general, polygon pours are used for ground and power rails. It depends on the layout and the requirements of the circuit. They are "just" copper and they can be used for many purposes: electrical connection, grounding, thermal relief, reference plane for a controlled impedance track, inter-plane coupling...
They can affect the performance of the GPS and BL as any other layout feature. They are part of the whole layout.
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Regarding your project, it sounds kind of complex PCB.
Before thinking about polygon pours you should sketch a first schematics and then start to think about the PCB.
Some questions that may help for the PCB design:
How many power rails do i need?
What are the power requirements of each power rail?
Do I have a fine pitch packages like BGA or QFN? How many layers do I need to fan out these packages?
Do I need any controlled impedance track for the RF section?
Probably you would need 4 layer PCB and consider controlled-impedance tracks.
Best Answer
IPC-2221 specifies recommended clearance rules for given peak voltages. Based on this calculator, per IPC-2221B you need a minimum of 13 mm (512 mil) clearance between the high voltage traces and surrounding copper/components, assuming your traces are on the top or bottom layer and are coated with soldermask.
When working with such high voltages, it is advisable to include a creepage gap as well - a slot in the board between the high voltage section and the rest of the board to prevent any arcs from tracking along the surface.
This combined with the above clearance requirement should help protect your board from undesired arcing.