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Your tree may not be quite old enough to bear fruit just yet - it can take up to 6 years. Does your tree get enough sun? Are there any signs of disease or insect infestations?

Here is an article that explains why plum trees do not fruit:

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

Happy gardening!

You can apply a fertilizer that is higher in phosphorous and potassium and lower in nitrogen in a slow release formula.
This will help promote good root growth and winter hardiness.
Less is more as excess fertilizer can be a stressor at planting time, so do not over-apply.

Watering is very important to get the new plantings established.

https://www.gardeningknowhow.com/edible/fruits/fegen/dwarf-fruit-trees-a-planting-guide-for-fruit-trees-in-containers.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/watering-newly-planted-tree.htm

Check the branches. Do they snap off and break or are they pliable?

The lower leaf you mention sounds like it is likely coming from the root stock.
My guess is that the tree died and the root system still has some life in it.

Check with the grower. Most reputable sellers will replace a new tree for one year.

This does sound like a bacterial or fungus disease.
It will take further inspection of the tree to make a determination and how to treat; or if you may need to remove the tree.
This article will help you access the tree.
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-diseases.htm

This looks to be one of several bacteria species that cause bacterial spot. This is a very general disease classification, and all have similar treatments. Most will not be cured, fully, but some can be. Either way, they can be managed.

You can try fungicides, but good sanitary practice and keeping all infected debris away from the area.

https://www.gardeningknowhow.com/edible/fruits/plum/managing-bacterial-spot-on-plums.htm

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm