Why did specifically the sun and moon bow to Yosef in his dream?
Maharal (Gevuros Hashem, Second Intro., p 15): The sun is physical (Chomer), and the physical is subservient to the intellect (Sechel). The sun bowed to Yosef, for Yosef rose above all physical matters. 1
Yosef ran away from immorality; he was Kadosh - above and apart from physicality. Therefore, the physical world was subservient to him - even the luminaries in the heavens. (EK)
Why did Yosef insist on repeating his dreams to his brothers, and to his father in their presence, even though he must have realized that this was bound to increase their hatred towards him?
Oznayim la'Torah: There are two kinds of dreams: Those that are caused by a demon - which are meaningless and which leave no impression on the person once he wakes up, and those that are caused through a Mal'ach, which are in the form of a prophecy and which (like prophecies) make a deep impression on the dreamer, and (like prophecy) make him want to tell it to people. 1 Yosef's dreams were of the latter caliber, 2 which meant that it was almost impossible to keep it to himself.
Refer to 37:9:151:1.
See Oznayim la'Torah, who supports this from the dreams of the butler and the baker, of Pharaoh and of Nevuchadnetzar.
Oznayim la'Torah (to 37:8): Which also explains the brother's negative reaction, since, on the one hand, they could not help but acknowledge that the dreams were destined to come true, while on the other, they tried to placate their burning jealousy by accusing Yosef of playing up his nonsensical dreams as if they were prophesies.
Pharaoh's dream was repeated as a sign that it would materialize immediately (see 41:42). Why did Yosef dream twice - bearing in mind that it took 22 years for his dreams to materialize?
Oznayim la'Torah #1: Yosef's two dreams refer to two different eras - The dream of the sheaves refers to the brothers' arrival in Egypt to purchase grain; that of the sun, moon and stars, to when Yaakov bowed down to Yosef at the head of the bed 1 and when the brothers fell before him to the ground, following the death of their father. 2
Oznayim la'Torah #2: In answer to what kind of ruler did Yosef think he would be, 3 his first dream indicated that he would be a 'Melech' (appointed to serve the people in time of famine), his second dream, that he was destined to be a 'Moshel,' an all-powerful monarch who would rule over them due to his majestic personality. 4
See Bereishis 47:31.
See Bereishis 50:18.
Refer to 37:8:1:1; 37:8:151:1.
See Oznayim la'Torah, who elaborates.
Why does it say about the first dream "va'Yaged" (37:5), and here it says "va'Yesaper"?
Malbim: Hagadah is relevant to the listener; Sipur is not. Yosef told his brothers that his first dream is relevant to them, and he they hated him due to this. The second dream includes his mother bowing to him, which cannot be. Surely it is not a prophecy; he merely tells them - and the same applies to the first dream, so there is no reason to hate him.