From multiple sources I've understood that vegetable peels, such as potato peels, can be used as fertilizer for various plants. What about fertalizing a plant with its own fruit, or another part, such as its root? Think of fertalizing a lemon tree with lemon peels, an avocado tree with avocado peel, etc. Is such practice advisable, more so than using a mix or a specific (foreign) type of peel (like potato peel)?
No, it is never advisable: most diseases are specific to a species or a genera, and many fungi diseases on fruits are usually propagates with fallen fruits (waiting the new fruits). For this reason, using the same type of peel, one risk to increase diseases.
Note: it is not only about diseases on peel, but also diseases which can find the compost a good mix (peel-like) to growth before going to fruits.
In any case, the fertilizers should contains the elements for peel, fruit interior, but also for leaves and trunk, so you see, peels are small optimization, but with too much risk.
Note: in wild, there is (nearly) never monoculture: plants require much more nutrients then the leaves and most of fallen fruits.