New Bathroom exhaust through roof

I currently have only windows in the bathroom and want to install an exhaust fan with roof vent. I can get into the attic area above bathroom, but really have to slither, there isn't much room to move.

I have a gable vent that is 5 ft away from where the bath fan will be.

Questions.
1. From my readings, it seems I should put the roof vent away from the gable, at least 10 ft or does that not matter?

2. Is going straight up from the bathroom vent a good idea? I Would only need 3 ft of flex or solid venting pipe. Or is there a certain distance away from the bathroom I need to go to lessen noise?? I think I read 10 ft? Common sense to me says get a shorter run, less resistance, less heat loss.

3. I live in the northeast and I am concerned with snow covering the vent, is there another kind of vent or do I not have to worry.

4. Rather than using flexible ducting, should I use metal? Can PVC be used? If I understood correctly you can't use pvv due to "IMC section 603.8.3 Plastic ducts and fittings. They are allowed for underground duct only."

I then read that a master plumber say he uses schedule 40 PVC pipe and send the exhaust up through the roof. Once the pipe exits the roof, use a gentle sweep 90-degree angle followed by a 45-degree bend to prevent rain water from entering the exhaust pipe. Be sure the end of the pipe is at least 20 inches above the roof so it's never blocked by deep snow.
The. He says he uses 3 inch foam insulation".

I would appreciate any insight. Thank you!