For your question about radius, we cannot disclose exact details of how geo-targeting works. What I can say is that we use multiple signals available to us to determine with confidence that a user is in the location that we then geo-target. Some of those signals do include the IP address the user is accessing Twitter from.
The biggest reason to see ads shown to a user in the ‘wrong’ city (from stats perspective) is earned engagements - someone can retweet and a follower from another city can see the same tweet, and it will show up in the list of cities on stats pages. I could imagine that some “errors” could occur based upon how user is traveling or connecting to the Internet but in general this is one of the core functionality of our system that should be the same between API and ads.twitter.com.
The questions around targeting combination, the logic is:
"Targeting criteria will be combined for your ad group such that:
“Primary” Targeting Types will get ∪‘d (i.e. put in a logical union).
Other Targeting Types will get AND‘d.
Same types will get OR‘d."
…from https://dev.twitter.com/ads/campaigns/targeting
So countries would be AND but themselves in an OR with each other. There is an example on that page which might help illuminate how it works. The idea is that some targeting is better for expansion (reach or recall) and some are better for filtering (precision).
