The pun is, "Santa arrived at the party just to the NICK of time." He's often referred to as "Saint Nick." The meaning of the pun, is, he made it to the party quick, or he made it just in time.
Answer:
1. Fresh
2. Tenth.
3. Check.
4. Cheer.
5. Shelter.
6. Shadow.
7. Birthday.
8. Chapter.
9. Thorn.
10. Bathtub.
11. Shape.
12. Thaw.
13. Chipmunk.
14. Short.
15. Couch.
Explanation:
These should all be correct, from what I know. Hope it helps!