What is the ruling on watching foreign programs or films that include women or music, for the purpose of learning the language for dawah (proselytizing) purposes, while striving to lower one's gaze and avoid forbidden things as much as possible?

It is not permissible to look at immodestly dressed women, nor to listen to music for the purpose of language learning, as long as it is possible to learn the language without them. Prohibitions are not made permissible except in cases of necessity.