This plugin will display your Amazon wishlist.
Yes, you can, just need to input the html code on layout area.
You probably have the cache option enabled, this option cache your wish list for 1 day to avoid request amazon every time you page receive a hit. Try to invalidate cache.
There is an option on pluging settings named
Invalidate cache, set it to on, and hit update, it will remove the cache file, forcing it to be recreated on next hit.