Question: in the dropdown menu, while I see a few countries, I can't seem to find the country (or region or city) that I want to segment.
Answer: this was more so a user experience decision in that it wouldn't be feasible to display all countries in the dropdown menu. All you need to do is start typing the country's name and it will autocomplete. Please see the screen capture below.
Here's how you set the country filter for Experiments
Here's how you set the country filter for Push Notifications