What is this teaser referring to

Question: My first is in yesterday, but not in today; My second is in after, but not in before; My third is in start, and also in stop; My fourth is the 20th letter of the English alphabet; My fifth is in correct but not in wrong; and my sixth is in pretty, but not in cute. My whole is something celebrated by Christians. What is this teaser referring to?

Question: What can be broken but never forgotten?

Question: People see through me, but none pass through without killing me. I can be anywhere, and can be seen double or single. What am I?

Question: Which thing that comes once in a year, twice in a week?

Question: You are trying to get your chicken, fox, and wheat to the barn. However, the barn is on the other side of the river. You are on a boat and can only transport one animal or wheat at a time. You must choose carefully not to leave the wrong two together, though. It's either the fox will eat the chicken or the chicken will eat the wheat. How do you take each thing across safely?

Question: During what month do people sleep the least?