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It isn't necessary. Most apples are self-thinning. You can still help it along, but it will do perfectly fine without it.

Here are some articles to help:

https://www.gardeningknowhow.com/edible/fruits/apples/apple-tree-planting.htm

https://www.gardeningknowhow.com/edible/fruits/apples/how-to-thin-apple-trees.htm

This is Cedar-Apple Rust. This disease can be managed, but not likely cured.

Here is an article that will help:

https://www.gardeningknowhow.com/edible/fruits/apples/how-cedar-apple-rust-affect-apples.htm

Here's an article about apple scab that will help: https://www.gardeningknowhow.com/edible/fruits/apples/treating-apple-scab-fungus.htm
Here's an article that will help you with your non-bearing pear tree: https://www.gardeningknowhow.com/edible/fruits/pear/no-pears-on-tree.htm

The times for spraying your trees are dependent upon your local weather and temperatures. The following is an article about spraying fruit trees: https://www.gardeningknowhow.com/edible/fruits/fegen/fruit-tree-spraying.htm

It's not that two dwarfs can't pollinate each other, but that it has to be two different varieties of the same species (apple). Two trees of the same variety won't cross pollinate. You need to find another dwarf of a different variety that has a similar bloom period. Your local Cooperative Extension office has tables that show what varieties will pollinate each tree.

Also, if a neighbor has a flowering crabapple, it can pollinate your tree.

Bare root trees can be planted when it's cool from fall to spring.

https://www.gardeningknowhow.com/garden-how-to/propagation/propgen/bare-root-planting.htm