What is the interpretation of a dream in which the father greets and embraces the suitor, and a dream in which wedding invitations are distributed after performing Istikhara? And is it permissible to perform Istikhara to ascertain the extent of the suitor's family's affection?

Istikhara (prayer for guidance) is prescribed when responding to a suitor, regardless of his family's situation, and nothing is contingent on a dream. If the young man is pleasing in his religiosity and character, then he should be approved, based on the hadith (definition): "If someone whose religiosity and character you are pleased with comes to you, then marry him."