So these are the tree-like things that can be hit to obtain certain things. If I am missing any, please tell me in a reply to this thread so I can fix it.
There is a banana tree in Port Fidelio (near the lighthouse).
There are special cacti scattered around the Whispering Dunes which drop Cacti Fruits.
There is an apple tree in Mushtown.
There are several pear trees in Nilgarf.
Bananas give temporary walkspeed and jump height boost
Apples and Pears give minor healing.
Cacti Fruit fully replenish Stamina bar (even outside of the Whispering Dunes).