1) Proper way I guess is one of those debatable or matter of opinion areas. The tank has to be vented so that air or something else really, takes up the space that was occupied by the fuel. If this doesn’t happen then a vacuum (low pressure) builds and can even become great enough to collapse the tank and kill the engine. For environmental reasons the old vented caps were sealed and the tank vented through a charcoal canister to capture the vapors. The charcoal canister is still vented, the tank has to be somehow. So yes, you can remove the canister but the line from the fuel tank still has to be open to the air or some other form of venting the tank made. The CIS pressure is after the pump and has nothing to do with the venting of the tank, unless it is not vented and fuel flow stops.
2) I guess it will only effect fuel mileage seeing as you asked it that way, but you will not notice any difference. The amount of fuel, in vapor form, burned is very very small and I doubt it would show up in checking your gas mileage. Power out-put would also not change as the missing bit of fuel will be adjusted for by the ECU upon any changes detected with the O2 sensor.
3) The ECU has no direct knowledge of the existence of the charcoal canister. If it is present or gone is something the ECU just can’t see. Its only knowledge would be any change in the exhaust gasses which really would be too small to detect I think and if it were then the ECU would just treat it as a normal mixture adjustment.
This all brings up the question “why”? It is almost invisible so you are not cleaning much up in the engine bay. It is almost trouble free as it is very simple and has few parts to wear or go bad. And many states would view it as tampering and fail you in an inspection I think. For any car driven on the street I just don’t see the benefit or reason for tearing it out. What’s your reason?