How to have a field with a select list widget and custom list entries?
For Drupal 8

Yes, is possible, but you will need to implement your own field type.

You should take a look into the Country module as you will need to implement the OptionsProviderInterface interface.

In the getPossibleOptions method, you will query the external site and get the possible options for your field.

For Drupal 7

You can always take a look inside the Examples module even for Drupal 8 you will find a very useful boilerplate code for your projects. If you want to check another example just go to the Countries module.