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No, they aren't.
Taking your question literally, these leaves are edible, the Little Leaf Linden or Lime Tree, the Fragrant Spring Tree from Japan and the Mulberry. There is also a Chinese tree called the Goji No. The fruit of a tree is the seed containing capsule. The leafs are the foliage edible or not.
carob
No, they're native from the peruvian Andes.
The Cleveland pear tree does not bear edible fruit. The Cleveland pear tree is named as such, due to the fact it's leaves are pear shaped.
A tree that grows pepper.
Peruvian Pepper or false pepper (Schinus molle) is and evergreen tree not to be confused with Pepper (spice) which is a vine not a tree.
The apple is a fruit. The apple tree, however, has roots, branches, leaves and flowers.
Papaya leaves and also the flower buds are eaten in Indonesia.They must be boiled (often with cassava leaves) to reduce their bitterness, then well drained and mixed with spices and freshly ground and roasted coconut flakes.
Pili is the edible seed in question.
I use Kaffir Lime Leaves all the time in cooking, it's just a matter of finding out which specific tree you're talking about and researching it.
The Brazilian Pepper Tree is a tree that does not require much care. The tree should be fertilized in the spring and watered as needed.