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When you get blossoms but no fruit, or when blossoms drop, this is normally an indication of poor pollination. If there are not enough natural pollinators around or if it's grown indoors, the tree will have difficulty producing. This is why we sometimes have to intervene by hand pollinating. Just use a small paint brush and swirl it around the inside of the flower and repeat on all the flowers on the plant. You can encourage additional pollinators to the area for outoor trees. Here is more information on that: https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm, https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm

Premature fruit drop is normally the result of poor pollination or an insect problem. Peach tree borers can also affect plums. This article will help determine if this is a problem: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm This article may help as well: https://www.gardeningknowhow.com/edible/fruits/plum/plum-trees-not-fruiting.htm Overbearing is another possibility. When the fruit is pea size, begin thinning to prevent fruit drop. This will reduce the energy of the tree so it can put more into the production of fruit. If pollination/fertilization is at too great a level for the tree to sustain, all of the set fruit will simply drop. You can also thin the blossoms rather than the fruit.

It is possible that your tree is aborting its fruit due to an over abundance of fruiting. This is normal and the reason why thinning is often performed on fruit trees. Fruit thinning (removing excess fruit) can help produce better quality fruit. Fruit should be spaced at least 4-5 inches apart. If they are closer than this, removing smaller fruit is advised.

It sounds like Phytophthora rot and your other trees do need to be treated. This article will help: http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn74133.html

First, I would dispose of the diseased plants, taking care to remove any debris within that area and I would probably avoid planting the new plums in the same area, just as a precaution. These articles should help: https://www.gardeningknowhow.com/garden-how-to/info/diseased-plant-disposal.htm, https://www.gardeningknowhow.com/edible/fruits/plum/black-knot-tree-disease.htm, https://www.gardeningknowhow.com/plant-problems/environmental/planting-in-old-spaces.htm, https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm

You are wise to not worry about fruit production at this stage, and to focus on correct pruning to ensure the future strength and health of your tree. This article will explain pruning procedures: https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-pruning.htm