Should weed control be sprayed around the base of an apricot tree, what are the orange growths protruding from the trunk and how should this mature tree be pruned
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: