What is the meaning of "Vatis'alaf"?
Rashi #1: It means that she covered her face. 1
Rashi #2 (Shir ha'Shirim, 5:14) and Targum Onkelos: She made herself look nice.
Targum Yonasan: It means that she wrapped herself in it (the veil).
Ha'Emek Davar: She wrapped a scarf around her neck, but it covered also her face, even at the time of Bi'ah. If not, Yehudah would have recognized her! 2
This is also how Rashi probably translates it according to the Midrash that he cites later (Refer to 38:15:2:2).
What forces him to say so? Even when Bi'ah is permitted during the day, it is only in a dark room, or he covers with his garment to make it dark (OC 240:11)! Perhaps he means until the time [that it was totally dark and proper] for Bi'ah. (PF)
What does "Pesach Einayim" mean?
Rashi #1: It means (that she sat at) the cross-roads. 1
Rashi #2: It means next to the opening of Avraham Avinu, where everybody tended to look. 2
Seforno: It means a fork in the road (the beginning of two roads). 3
Ha'Emek Davar: In these lands there are no inns on the road, only an empty house in which no one lives. One who needs to lodge overnight stays there. There are empty beds there.
Sotah, 10a #1: "Einayim" is actually the name of a town.
Sotah (10a) #2: It means that she gave 'eyes' (answers that permitted her to Yehudah) to the questions that Yehudah asked her when he accosted her - 'Are you an idolater?' - 'I am a convert (to monotheism).' 'Are you married"? - 'I am single'. 'Did your father accept Kidushin on your behalf?' - 'I am an orphan'. 4 'Are you Tamei (a Nidah)?' - 'I am Tahor'.
Targum Yonasan: It is where everyone looks. Na'ar Yonasan - whoever passed by would be bound to see her, predominantly Yehudah, who, she knew, would shortly arrive there.
'Mizrachi - i.e. Me'aras ha'Machpeilah, where he is buried. Maharsha (Sotah 10a) - the Gemara connotes that it is the opening of his tent. See also Ba'al ha'Turim.
So that whichever road Yehudah took, he could not avoid seeing her.
Maharsha (10a): My father died before I was born, so surely he did not accept Kidushin for me. Rashi (Sotah 10a) says that she was a minor (unlike the opinion that she was Shem's daughter - PF), so she never married his sons [mid'Oraisa]. Da'as Zekenim (26) - she did Mi'un to nullity it retroactively. [We can even say that she was Shem's daughter,] like the opinion that an adult can do Mi'un (That is only for mistaken Kidushin (Yevamos 100b)! - PF) Some say that Tamar was single, for only Bi'ah k'Darkah makes marriage for Bnei Noach. This is wrong. All agree that with a husband, even Lo k'Darkah makes her Be'ulas Ba'al.
Why did Tamar do what she did?
Rashi and Ramban: Because she wanted to have children from Yehudah. 1
Seforno: She intended to draw the attention of Yehudah that he should arrange for her marriage (Yibum) with Shelah, seeing as he had grown-up and was fit to do Yibum with her. 2 This she did by changing out of her widow's clothing - that Yehudah himself had instructed her to wear in the interim. 3
Refer to 35:14:151:1.
Ha'Emek Davar: She wanted to ask Yehudah to give her to Shelah.
Seeing as he declined to take her as a wife for Shelah.
In accordance with his own instructions in Pasuk 11.
Why does it say "Hi"? This is not needed?
Ohr ha'Chayim: Clearly she was not given to Shelah. "Hi" hints that she saw through Ru'ach ha'Kodesh that it is not proper that she be given to him for a wife, therefore she did [what she did] and succeeded. Look at what resulted!
Why did she remove her widow's clothing?
Seforno: Refer to 38:14:3:2.
Malbim: She showed that she did not want to do Yibum. Since she was not given to Shelah after he matured, she was exempted from Yibum. She wanted to talk to Yehudah that he should marry her.
QUESTIONS ON RASHI
Rashi writes that she sat at the cross-roads. Even the lowliest prostitute would not do such a thing!
Yerushalmi, Sotah, 1:4: It must mean that Tamar turned her eyes Heavenwards - to the opening which all eyes hope for - and said 'Master of the world, Do let me leave this house empty-handed!'