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It depends on the type of plum. They can be pink, yellow, green, red, orange, or anything in between! There are many varieties.

This collection of articles will be helpful to you: https://www.gardeningknowhow.com/edible/fruits/plum/page/3

Sanitation is important, Pick and dispose of all fruit "mummies" , from the ground also, and plant debris. Prune out obvious infected growth.

Use a dormant spray in winter with horticultural oil and fixed copper. Fertilize with a complete organic fertilizer:

This subject is, actually, a little more complex than it should be. This article will help to get you started: https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-pruning.htm

Your country doesn't seem to get cold enough for any of the prunus species to drop leaves. In fact, most of the species could very well fail to fruit in your country, since it lacks a time where the temperatures spend several months below freezing. There are only a few species of plum that will do well, and only a handful of nectarines, so you will have to make sure that what you have is bred for your area. If you plant from seed, then you won't likely get your target fruit, since they willingly cross pollinate.

I would say that your tree is perfectly fine, and is reacting as it should given the environment.

https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm

https://www.gardeningknowhow.com/edible/fruits/plum/plum-trees-not-fruiting.htm

Sterilizing trees requires chemical means. If I am not mistaken, most if not all of these are banned in your state.

Unfortunately, there isn't much you will be able to do, unless you pluck the flowers before they turn into fruit.

Here is an article that will offer more information: https://www.gardeningknowhow.com/ornamental/trees/tgen/fruit-tree-sterilization.htm

The "spot on the barn"? appears to be a wood decay fungal infection at the site of an old wound or pruning cut.. We can't see the entire tree so we assume that it is most likely a local infection at that spot on the tree trunk and not greatly affecting the overall health of the tree.

The only thing that you can do is to keep the tree as healthy as possible to help it resist advance of the infection and close the wound. Do that with good soil fertility and water management.

https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm