What's your question? Ask

It really depends on the symptoms you are seeing. This article discusses common apple problems, if you have not already seen it: https://www.gardeningknowhow.com/edible/fruits/apples/apple-tree-diseases.htm

Any chemical that one would use to control the root suckers would almost certainly wind up effecting the main roots of the tree. Thus a chemical is really not the way to go. The best thing you can do is to cut the root sucker out as far down and back towards the tree as you can and place some Elmers regular white glue on the end of it, not the school glue but the regular kind. Let it set of a few minutes and then cover back over with soil. The glue will sometimes help prevent off shoots from the same area that brought forth the root sucker. Does not always work in very hardy trees and shrubs but is worth a try.

Most planting should be done in spring (exact month depends on where you live and after frost), especially people living in northern climates, while those in southern regions should do so in fall, usually anytime between Sept. and Nov.

It will not hurt the tree to remove these shoots now, or fall, as they will only sap energy and nutrients from the tree. However, all other pruning should be done while the tree is dormant. For future reference, this article should help: https://extension.psu.edu/plants/gardening/fphg/pome/pruning/pruning-a-special-case-renovating-old-fruit-trees

You don't need to keep them separated. The only time there is a concern with cross pollination is if you plan on growing the seeds from the fruit.

For trees in containers, you want to have a reasonable distance of a few feet between, just so there is good airflow on the plants, but other than that, there is no reason or need to keep them apart.

It sounds like a fungus, possibly sooty mold. A general fungicide should help, but if it does have a sooty appearance, it means that you also have a pest problem like aphids. You will also need to treat the tree with a pesticide as well if this is the case.