Translation:My father lives in a foreign country.
It's possible to drop the my, but it sounds a bit strange to my American ear. If you just say "father" without the "my", it sounds like you are talking to your own family members. The Japanese sentence has the opposite implication, that you are talking to someone outside of your in-group.
In English, when we say where we currently live, we use the present tense (I live in Hokkaido). In Japanese, when we say where we currently live, we use the present progressive tense (北海道に住んでいます Hokkaido ni sunde imasu). Using the present progressive in this special case is equivalent to the present tense in English.
Except that we'll use that present progressive ("Fred is living in Japan") when we want to emphasize something right now. For example: - Anne is living in San Francisco (military posting, school, etc.; moving again is not unexpected) - Bart lives in Georgia (married and settling down, perhaps in a new place)
The point is that "is living" is quite reasonable as a translation in this sentence, depending on things like context (which we don't have).
As long as everyone understands that the Japanese doesn't have the same distinction, and that if you say "chichi wa gaikoku ni sumimasu" it doesn't mean the same thing in Japanese. You must say "sunde imasu".
If you type in "my father is living overseas" and get it correct, you might never check the comments and realize the difference.
If you say 父は外国にすんでいます, you are saying that your father lives in a country that is not Japan. The listener doesn't know which country your father lives in. The important information is that your father lives in a different country, but it can be any country. It is not a specific country, so it is "a foreign country".
Thank you very much. I understand your explanation. In other question, "I bought a pen at the store." is correct. The listener does not know which store this person bought. Also, native English speakers say "I went to the bank." even though I do not know which back they go. It is very difficult how to use an article.
You're right, it's difficult to understand and it's difficult for me to explain! If I say "I bought a pen at the store" or "I went to the bank", the speaker usually assumes the listener knows which store or which bank. It's the store we were just talking about. It's the bank I always go to.