can other players scan another player PI structures on a planet ?
No they cannot. You can see other command centers on planets but that’s it.
Yes you can see all structures of other players if you turn their visibility on.
The only thing that remains invisible is the extractor heads.
Rightclick the planet to see that toggle:
Top left: my own setup. Bottom right: setup of another character. Looking at the way it’s setup, probably one of my alts
Or this other planet where I found two command centers, neither of which are my own:
You have to click the command center to see all the structures belonging to that command center. The player at the top there has spent a lot of link on putting their left extractor that far. Below it is another command center that isn’t selected, so you don’t see their structures.
If you find one you can even rightclick on the command center to see the owner’s name (censored here):
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What skills and to what level do you have to have them trained to be able to see others structures?
Asking because I’m just getting interested in PI and I can’t see anything.
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It’s surprisingly hard to find them, planets are big and the command centers not very visible.
For years I thought the button did nothing.
It’s also possible that no other players have set up PI at that particular planet.
I don’t think it’s skill related, none of the skills mention this.
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OK, thanks.
PI system doesn’t seem to be all that intuitive but maybe that’s just me being a slow learner
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If you want to do PI properly, Command Center Upgrades and Interplanetary Consolidation have to be V, and the others should be skilled up to V later, too.
Spotting other players’ structures is very hard. But as setting up new planets is quite cheap, you should just choose spots and give it a try.
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Play for your life in a wh and you learn real quick! 
Yeah, I figured I’d just start with one planet and work it out as I go.