Hi again,
Mmmm... After comparing your code with mine, I can see some differences.
For example you are populating this control with an List<string> using the AutoCompleteSource property:
countryAutoComplete.AutoCompleteSource = countryName;
In my case i'm using DataSource property, which is a List<object> and also using DisplayMemberPath property to display text values of those objects.
In Android and iOS is displaying a dropdown with no problem. Also tried with XAML with same results. Perhaps it is a bug for the WinRT version?