Why did the ass take Bil'am to task only after the third time?
Na'ar Yonasan: Because it was only after the third time that Bil'am struck it with his staff (the first two times, he struck it with a strap - Oznayim la'Torah). 1
See Na'ar Yonasan and Oznayim la'Torah.
Why did Hashem cause the ass to speak? Why could the angel not have told Bil'am the same things?
Seforno and Oznayim la'Torah #1: To teach Bil'am that Hashem is the Master of speech - and if He can make an ass speak, He can certainly prevent him from speaking, should He so wish. 1
Oznayim la'Torah #2: Because had the angel opened the same conversation, Bil'am would have answered 'Chatasi' - end of conversation; whereas now he made a fool of himself in front of the princes. 2
Oznayim la'Torah #3: Because we learn from his conversation with the ass a. that he was a liar 3 ; b. that he was a pervert; 4 c. that his claim that he knew the Mind of Hashem was untrue, 5 and (citing the Zohar) d. to counter those who say that animals are wise and if only they could talk, they would emit pearls of wisdom. See how the ass, whose miraculous mouth Hashem created independently Erev Shabbos at dusk, and when it spoke, all it had to say was 'Why did you strike me? ... '. 6
To demonstarte to the world that he could not even fathom the mind of his ass 7 (let alone the Mind of Hashem, which he later boasted he knew). 8
Seforno: And He did this in order to prevent such an important personality from destruction. Refer also to 2:22:2:1.
Refer to 22:30:1:1**.
Refer to 22:29:1:2*.
Refer to 22:30:1:2 & 24:16:1:1*.
How will we reconcile the ass speaking with the principle that, since the time of the creation, Hashem never created anything new?
Targum Yonasan and Avos 5:6: The mouth of the Hashem created ass is one of the ten miraculous things that Hashem created Erev Shabbos at dusk. 1
Targum Yonasan: The other nine are the Manna; Miriam's well; Moshe's staff; the Shamir ('worm'); the rainbow; the Ananei Kavod; the mouth of the earth (of Korach),; the writing on the Luchos; and the Mazikin (demons). Avos includes also the Luchos and the stylus used to write them (Rashi; Rambam, R. Yonah ? the writing of the Torah), and excludes the Ananei Kavod and [according to one opinion] the demons.
Why did the ass use the expression "Shalosh Regalim" rather than "Shalosh Pe'amim"?
