Pesachim 9:4

If most of Klal Yisrael is tamai from a corpse, the korban Pesach can still be brought and eaten.

Even though the korban is broght with tumah, still a zav, zava, niddah or a lady who just gave birth to a child, cannot eat it, but if they did they are not punishible by kares. R’ Eliezer says even if they walk into the Bais Hamikdash, they are not punishible by kares since tamai meis can go in for the korban pesach.

Pesachim 9:5

When they went out of Mitzrayim, the korban pesach was guarded from the 10^th of Nissan, required sprinkling with hyssops on the lintel and 2 doorposts, and was eaten hurriedly, whereas the Pesach from then on did not have these laws.

Pesach after they left Mitzrayim is a Yom Tov for 7 days.