Why didn't Yosef, who was extremely strong (as we will see in Vayigash), grab his cloak from his mistress before fleeing?
Ramban: Out of respect for his mistress.
Why does it say "va'Yanas v'Yatza (he fled and went outside)"?
Seforno: Yosef initially fled from the room in order not to be overcome by the Yeitzer ha'Ra. Once outside, he walked, to avoid suspicion that he had done anything wrong.
Hadar Zekenim: "V'Yatza" in the merit of "va'Yotzei Oso ha'Chutzah" (Bereishis 15:5-6 - and Avraham believed).
Da'as Zekenim (15): In the merit of va'Yanas, the sea split in front of Bnei Yisrael. "Ha'Yam Ra'ah va'Yanas" - when it saw Yosef's coffin. 1
What stopped Yosef from sinning?
Rashi: The image of his father appeared to him 1 and deterred him from sinning.
Hadar Zekenim (11): It says "Ein Ish" - he checked and found that he has no male organ. Hashem did so to prevent him from sinning.
Why does it say "Leimor"?
Peninim mi'Shulchan ha'Gra: When she saw that he refused, she asked him to say "lie with me." This would make him more prone to sin. 1
מכח מה הצליח יוסף לעמוד בניסיון?
מהר"ל (חידושי אגדות ח"ב, עמ' עג ד"ה עתידין, סוטה דף לו:): דמותו של יעקב נראתה לו, ונאמר לו שהוא לא יהיה ראוי להכתב על האפוד אם יחטא, כי בעל זנות הוא חומרי ואין דבר יותר קדוש מהאפוד.