Campagnolo single speed conversion - can I use a 10sp cog?
Yes this is possible with a free-hub style hub, but you may run into some issues.

You can use a sprocket from a 10 speed cassette, and replace the other sprockets with spacers. You can place the sprocket in the spacer stack to achieve good chain alignment. 

I don't know how Campagnalo cassettes are built but Shimano cassettes combine the largest sprockets onto a spider, so you would not be able to use those individually.

Cassette sprockets are of course designed to enable the chain to come of them easily when shifting, so they are not as good as retaining the chain as a purpose made single-speed sprocket. For the same reason you may have an issue with the chain coming off the chainring without a front derailleur. This is why 1x systems use a 'double-wide' chainring for better chain retention.

Sheldon Brown has a page that deals with single speeds: https://www.sheldonbrown.com/singlespeed.html, find the section titled 'Cassette Hubs'.