Why did Rachel decline to rise before her father, and why did Lavan accept her excuse?
Ramban: Perhaps she tended to feel exceptionally weak during her period, as some women do - particularly those who have few children, who suffer from a lack of blood (low blood pressure? - EC). 1
Ramban: The early generations, in their wisdom, tended to keep away from Nidos, 2 since they knew that their very breath was damaging, and that even their look was harmful, 3 which explains why they generally stayed at home and why people kept away from them. 4
Oznayim la'Torah (citing the Midrash Rabah): Lavan did not accept her excuse - "Va'yechapeis," and he (made her rise and) actually searched underneath the 'Kar ha'Gamal.' "But he did not find them" - because a miracle occurred and they turned into jars - in order to spare Rachel the embarrassment.
Indeed, that is why they are called 'Nidos' (See Rosh Hashanah 26a).
See Ramban, who elaborates.
And that is also why Lavan declined to answer her.
How could Rachel say "Derech Nashim Li" (I am Nidah)? She was pregnant, for she gave birth on the road!
Tosfos ha'Shalem (2) #1: She lied to him. 1
Tosfos ha'Shalem (2) #2: She became pregnant right after, and gave birth after six months. 2
Moshav Zekenim, Divrei Eliyahu, Kol Eliyahu: Idolatry is equated to a Nidah - "Tizrem K'mo Davah" (Avodah Zarah 47b. Since she is sitting on idolatry; she has Tum'as Nidah with her.)
Moshav Zekenim, Divrei Eliyahu and Kol Eliyahu ask how she could lie. What is difficult? Her justification to steal justifies also lying, and especially after Yaakov said "Lo Yichyeh"! (PF)
Yaakov's trip home took two years, including 18 months in Sukos, before Rachel gave birth! (Megilah 17a, Refer to 33:17:2:1). Perhaps Tosfos ha'Shalem holds like the Ramban (to Vayikra 18:25), that Yaakov never transgressed Achos Ishto in Eretz Yisrael; if so, she must have been pregnant before they came to Sukos. Harchev Davar (to 33:7) brings so from the Zohar. We can resolve this with Megilah 17a (without saying that her pregnancy exceeded 18 months), if [the Torah is out of order, and] she gave birth six months after leaving Lavan, before Yaakov came to Sukos. (PF)
Why is "Lo" spelled with Vov and an Aleph?
Moshav Zekenim: This hints that it is read both ways - I cannot rise due to the Terafim, but I could rise for someone else. 1
Why in the preceding verse does it say "va'Yemashesh" (31:34), and here "va'Yechapes"?
Malbim: He searched first for other thefts, and afterwards for the Terafim. 1 "Chipus" is searching for a particular matter.
What does "Yichar" mean?
Ha'amek Davar: It is an expression of anger only when it says 'Yichar Af.' Rather, it is being heated; when one stares at something, it heats the eye. Lavan was staring at her - why is she not rising?