To get a golden egg, talk to your chicken and pet her everyday. Wait a bit and you will get lots of eggs!
Easy Marriage For Celia: give her a tomato with a flower everyday. Thus you will get 4 hearts and a heart at the end of the sentence in her diary.
Awesome Catch: go to turtle swamp and fish for a long time to catch a Yamame. Thus you can get from 500G to 1000G.