Click here this thread should answer the question.

Yes. Crabs - and pretty much any crab - are excellent apple pollinators. As long as the bloom times coincide.

What do you consider 'small'? Your list of choices may stay somewhat narrow but not at all small in stature. And narrow doesn't provide a high degree of shade relief, regardless of height. Planting in multiples is also likely to overwhelm what is essentially a tiny plantable backyard. Small trees for small spaces generally are best kept to under 20-25 feet - crabapples, redbuds, most dogwoods, Asian maples, hawthorn, some magnolias. The question is will these provide sufficient shade to be of value and will they spread too wide to fit in that narrow planting area? I wouldn't be overly concerned about the possibility of Verticillium wilt being present in the soil. It is in most soils but stays dormant until prompted into activity by a stressed or damaged susceptible woody plant. I've experienced VW where it has killed a susceptible species but completely ignored several others very closely adjacent. Just don't plant a susceptible species in the same location as one that was infected and died and you should be fine. tbh, the suggestion of a shade sail or awning or even a pergola if the budget allows makes the most practical sense.

A crabapple IS a regular apple tree.........just a different type of one. There are several species of crabapples but only one species of orchard apple, Malus domestica. Since you can't change the species of an existing tree, your crabapple will always remain a crabapple. If you want a regular or orchard/grocery store apple, you will need to purchase and plant a cultivar of Malus domestica.