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Although these are self-fertile, it is best to have more than one tree, as cross pollination will ensure fruit production. Usually this is the case. Many people who only have one tree have this same issue. Here is an article that will help: https://www.gardeningknowhow.com/edible/fruits/apricots/apricot-tree-not-fruiting.htm

It is possible to cultivate the new trees in containers, if you can accommodate them with large enough pots for trees that size. It's usually better to plant in the ground for long term growth.
If the root mass that you are trying to dig through is from the pear trees that you removed (and not from a living tree) you could consider hiring a local tree service with a "stump grinder" machine to grind a hole out for you.
Otherwise, the path of least resistance and lowest cost may be to choose another area of the garden.

Avoid the weed killer near the tree. Some chemical herbicides can enter the tree's absorbing roots or directly through the bark and harm the tree. It appears to be a small enough area that you could easily and effective remove the grass by hand weeding. Or preferably use a 2 or 3 inch layer of organic mulch.

The growths on the tree trunk appear to be fungal fruiting bodies (conks from a bracket fungus - basidiocarp) indicating an internal wood rot fungus infection. I don't know the exact identity of the disease, but a local arborist or university extension pathologist may be able to help you identify and recommend treatment if available.

Pruning lessons cannot be achieved in an email, but in general I would say just to thin and lightly shape the foliar canopy. This article may help you get started:
https://www.gardeningknowhow.com/edible/fruits/apricots/pruning-apricot-trees.htm

It is important to remove dead branches as they are an invitation to pests and diseases. But it is also important to do it at the right time of year and do it properly or you'll injure the tree. If you've never pruned a tree before, think of hiring a professional arborist who has to right tools to do the job correctly. This article discusses apricot pruning: https://www.gardeningknowhow.com/edible/fruits/apricots/pruning-apricot-trees.htm
Identifying the "branch collar" is critical to successful healing of the pruning wound. (Do not paint the wound.) Look at some online videos on tree pruning to learn to identify the branch collar and how to correctly remove limbs.

Forgot to add to my post - I do not know the variety of apricot. (& don't know why the photos changed their orientation during upload). Tim