Why didn't Yosef, who was extremely strong (as the Midrash describes in Vayigash), grab his cloak from his mistress before fleeing?
Ramban: Out of respect for his mistress.
Oznayim la'Torah: It wasn't from his mistress that Yosef was fleeing but from the Yeitzer ha'Ra. 1
As Chazal said in Avos 1:4 - 'Hevei Bore'ach min ha'Aveirah!' And the Mitzvah of running away from the Yeitzer ha'Ra protected him from harm - 'Shomer Mitzvah Lo Yeida Davar Ra' - and his cloak in the hands of his mistress turned out to his advantage, as the commentaries explain - Refer to 39:20:3:6*.
Why does it say "va'Yanas va'Yetzei" (he fled and went outside)"?
Seforno, Ha'Emek Davar: Yosef initially fled from the room in order not to be overcome by the Yetzer ha'Ra. Once outside, he walked, to avoid suspicion that he had done anything wrong. She did not know this, and assumed that he will tell people that he fled her seduction.
Hadar Zekenim: "va'Yetzei" on the merit of "va'Yotzei Oso ha'Chutzah" (Bereishis 15:5-6 - and Avraham believed).
Even though some explain that Yosef needed miraculous help to refrain from sinning (refer to 39:12:3:1, 2), surely he received the help due to his awesome merits! (PF).
As the Pasuk writes in Tehilim "ha'Yam Ra'ah va'Yanas!" See Oznayim la'Torah as to why the merit extended to the whole of Yisrael.
Why does the Torah add the word "Leimor"?
Peninim mi'Shulchan ha'Gra: When she saw that he refused, she told him 'say "lie with me."' This would make him more prone to sin. Above (verse 7), "va'Tomer (she said) Shichvah Imi." 1
Ohr ha'Chayim: This was her intent. Actually, she did not say anything. She only grabbed his garment to force him.
This explains why it says here "Shichvah" in the feminine. However, it does not explain why it says "Shichvah" also in verse 7. (PF)