Logic Riddles

Question: what is small but can save things that do not weight anything in it?

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 goes up AND comes down?

Question: I was going to St. Ivor when I came across a man with 7 wives and the wives had 7 sacks and in those 7 sacks were 7 kittens and with those kittens were 7 kits. How many went to St. Ivor?

Question: Disgusting and small, we wriggle through your halls, devouring books, cloths and walls. Alone we are feeble, together we have some might, glinting in our damp holes at night. What are we?