Pros and Cons of shooting 1080p "NTSC" in PAL region?

First up - NTSC and PAL are analogue video systems and do not exist in SDI (Digital World). SDI can be SD-SDI or HD-SDI (Standard definition and High definition) respectively.

Why the camera manufacturers still refer to system settings as NTSC or PAL fails me.

It all all one system now and with SDI you can choose the frame rate you desire to film with.

Yes, correct, more frames per second, the more info recorded, the bigger the file. (If the only change is the frame rate)

Yes you are correct, the higher the frame rate the smoother the motion is.

Best practice is, Shoot, edit and export in the same frame rate, resolution, codec and file format throughout the workflow.

That is why originating on .mov for editing on Apple Computers and FCPX is my first choice. (Unless shooting RAW)

If you going to edited and export at 25 fps, then you might as well shoot at 25 fps.

Or edit and export at 29.97, then shoot at 29.97 or 30, then shoot at 30 or 50 then shoot at 50 and so on.

UNLESS, you want to slomo the footage you shot in your edit, that will be a good reason to shoot at 29.97, 30, 50, 60, 100, 120, 240 so that the slomo will be at a higher quality than if you slomo footage shot at 25 fps which will digitally create frames.

Also for the best rendering of slomo footage make sure that you select:-

29.97/30fps recordings outside US/Japan can create flicker & 'moving lines' under artificial lights, esp. LEDs, 'cause AC has 50Hz.

Use 50fps in the UK …

… but:

higher frame-rates give that 'electronic' feeling to video, due to faster shutter-speeds, also known as 'soap opera look' - some like it (Peter Jackson made THE HOBBIT in 48fps), some hate the lack of motion-blur …

If it's real NTSC it's 29.97 not 30. Never a good idea to mix frame rates obviously as the clips have to be processed to confirm to the project. The results can be less than great, especially if there's motion or panning involved. I'd stick to 25 if I were there, or use 50 if that's available and you want less motion blur on movement.

Apologies, I meant to type Optical Flo before :- and the screen grab shows normal because I did not have footage selected so it is greyed out. To recap Optical flow is the best render. You correct, Normal is frame "doubling"