All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If an institution for Da‘wah (calling to Islam) provides the travelling expenses of a caller to Islam to a certain place and he wishes to manage some of his private affairs in that place, it is permissible for him to do so. However, it is impermissible for him to spend this money on something that it is not allocated for or to choose a country only because he has private affairs to manage there while other countries are more deserving of Da’wah. If he heeds these two prohibitions, it would be permissible for him to manage his private affairs as long as doing so does not negatively affect his mission.
Allaah The Almighty allowed those going to perform pilgrimage to trade; He Says (what means): {There is no blame upon you for seeking bounty from your Lord (during Hajj).} [Quran 2:198]
As for the second question, if a caller to Islam or a knowledge seeker was given traveling expenses when he travels to a country to do Da‘wah or to seek knowledge, such expenses would not be considered a return for doing Da‘wah or seeking knowledge. Rather, they would be considered an aid for him to do a good deed. Allaah The Almighty ordered us to co-operate with each other in doing good deeds; He Says (what means): {And cooperate in righteousness and piety, but do not cooperate in sin and aggression.} [Quran 5:2]
Allaah Knows best.