Advice on Nikon V1 camera?

I know that generally for landscapes you should set apertures of about f8-22 but that applies for full-frame cameras. Would it be safe to say that for a much smaller sensor size like the V1 I can get away with f4-5.6 and also to minimize diffraction?

Yes you could say that. Landscape photographers use small apertures to get a wider depth of field, so everything is in focus from close up to the distant subject, smaller sensors give you that wider depth of field at larger apertures when using the same lens.

Crop factors work with depth of field too, your camera has a crop factor of 2.7, then if a full frame sensor gives you the DOF you need at f8, on your sensor you will get the same DOF at f2.9 (f8*2.7).

This is the reason why using cameras with smaller sensors it's much more difficult to get the opposite, narrow DOF effect in selective focus shots, where the subject is sharp, but the background blurred.

It's also true that smaller sensors hit the diffraction limit by the same amount, on a Pentax Q (an extreme example with a 5.5 crop factor) you can't set lower than f8 using the systems lenses on them. If you use an adapted lens then below f8 you'll get diffraction at any smaller aperture. But in DOF terms f8 on a Pentax Q has the equivalent DOF that f44 will give you on a full frame sensor, (5.5*8=44), so it's not really a problem.

Smaller sensors also have this wide DOF advantage when shooting Macro. It's a disadvantage if you want a narrow DOF as in 'selective focus' shots.

You've answered your own question correctly. Yes, diffraction sets in earlier on smaller camera sensors. For full frame 35mm cameras, diffraction start to get noticeable around f8-11.By f16-22, sharpness is lost no matter how good of a lens you have.

With the 1" sized Nikon V1 sensor, you'll see diffraction over f5.6. Since your sensor is smaller, you'll have a decent amount of depth of field at f4-5.6.

- I shoot full frame with a Canon 5D mkIII for work. I also own a Nikon V1 that I use for family photos and traveling.