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Crabapples, however, are bred for their flowers. Some varieties are sterile and do not set fruit no matter what pollen is available, but the Adams crabapple is self-fertile. Adams crabapple flowers set fruit when they are pollinated by other flowers of the same tree.
Plant the Adams crabapple in full sun in well-drained, acidic loam soil, either as a specimen or in small groups.
https://www.gardeningknowhow.com/ornamental/trees/crabapple/flowering-crabapple-trees.htm

This article may help with that: https://www.gardeningknowhow.com/ornamental/trees/tgen/fruit-tree-sterilization.htm

From the symptoms it sounds as if your crabapple has apple scab caused by the fungus Venturia inaequalis that also infects eating apples.
These links have more information.

https://www.gardeningknowhow.com/ornamental/trees/crabapple/flowering-crabapple-trees.htm
https://www.extension.umn.edu/garden/yard-garden/trees-shrubs/managing-apple-scab/

Yes, crabapples make a good compost ingredient. Just make sure that your compost pile heats up enough to kill the seeds in the crabapples, or they could sprout and become a weed in your garden later on. This article discusses ways to help compost heat up:
https://www.gardeningknowhow.com/composting/basics/heating-up-compost-pile.htm

Although I'm not a lady... I do believe I can help you with your problem! Ha ha :)

So, what this appears to be, is a bacterial, or fungal issue. Fortunately, this can be an easy fix. I have a personal recipe that I like to use for both soil infections, and insects. You don't have to have every ingredient, but when you do, it is unstoppable. My recipe is as follows:

First, you will want to prime the ground with dolomitic lime, then spread wettable sulfur to Kill off any infection in the soil. I Also like to spray the plant itself. Mix a few drops of one or more of these ingredients into warm water with a spoonful of coconut oil: Rosemary oil, lavender oil, neem oil, garlic oil, cinnamon extract/oil and for really bad cases, also add clove oil.

This really depends on your climate zone. Generally early spring is the best time to plant these. When the temps stay around 50 or 60F degrees is when they like to be planted. Here is an article that will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/trees/crabapple/flowering-crabapple-trees.htm