Regarding when the angels visited Abraham and he asked Sarah to prepare the food for them, he asked her to prepare cakes but the cakes never came. Rashi says it was because she became nidah and thus the cakes were not pure enough to be served. My question is: Hashem spoke to Abraham about being the father of a nation 3 days before the angels came to his tent. Abraham most likely told Sarah. Sarah became nidah before the angels announced her future pregnancy, while preparing the cakes. If so... 1. what’s rashi source to say she was nidah? 2. if she already knew she would be the mother of a nation and became nidah while preparing the cakes, why did she laugh? 3. if it was (profetically) pessach, why did abraham ask her to prepare cakes?

Chag Same’ach! The real answer to your questions is the rule that one doesn’t ask halachic or historic questions on the aggadot (stories) found in the midrash, which are clearly not intended for halachic nor historic accuracy, and it's not uncommon that midrashim contradict each other and even contradict halacha, not to mention history (Tik. Zoh. Chad. 166; Rambam, Introd. To Guide for the Perplexed; Nodah B’Yehuda, Y. D. 161). The Rambam, Maharal and many others even ridicule those who take midrashim literally and at simplistic face value. That being said, according to the pshat, Avraham did not (!) tell Sarah about the impending prophecy, and that’s why she laughed when she heard it for the first time from the angels. Rashi’s source that Sara became nida, is the midrash which explicitly addresses one of your questions: what happened to those cakes, and why weren’t they served? Similarly, when the midrash says that it was Pesach, the drasha is based on the fact that Lot served matzot to the angels, and one opinion that Yitzchak was born a year later in Nissan, but it’s not necessarily historical. Nevertheless, even for those who want to take the midrash literally, matzot are also explicitly (!) called "ugot" (Shmot 12, 39), which is the same word used here. Though it's often translated as "cakes" (and so it's used in modern Hebrew), but it literally means "round" baked-goods, which includes matzot. Chag Kasher v’Same’ach! Rav Ari Shvat