Here is every collectable/secret from patch v0.7.0 in Wobbly Life.
Pets
To unlock Golf Ball pet you need to talk to him in his cave. To enter his cave you need to jump into the middle hole.
To unlock Unspeakable pet you need to talk to every statue in this order.
Observatory Code

Then you need to go to the place that is gonna be shown on the big screen and bring the item you find there to the observatory lady.
Museum Collection
Presents
Thanks to Casper and Hunie for his great guide, all credit to his effort. you can also read the original guide from Steam Community. enjoy the game.