Just wanted to let you know I haven't forgotten about your question.  Our entomologist and plant pathologist are consulting on possibilities.

The plant is a species of Juniperus and it looks like Eastern Red Cedar, Juniperus virginianae, based on the pictures. The orange substance is the spores of the cedar-quince rust fungus Gymnosporangium clavipes. This fungus spends part of its life cycle on Juniperus species, such as Eastern red cedar, and the other portion on rosaceous hosts (e.g. crabapple, apple, pear, quince, hawthorn, serviceberry, etc.). (Arborvitae is not susceptible.)

The cedar-quince rust fungus colonizes stems of Juniperus spp. Stems later develop cankers in the affected areas. Dieback may occur above the canker or the colonized area may continue to expand in subsequent years. When twig infections are numerous, the tree may lose vigor and thin out, particularly when trees are shaded. In spring, orange spores form on Juniperus species and are spread by wind to rosaceous hosts. Later, in mid-summer to early fall, the fungus reproduces on the rosaceous host, and spores from the rosaceous host are then blown back to junipers.

The normal control recommendation for junipers is simply to prune out affected stems as they appear; however, in this case, there are significant infections directly on the trunk, so this recommendation would not be practical. Fungicides generally are not warranted on Juniperus species; however, preventative fungicide sprays may be used to protect new growth, beginning in mid-summer and continuing through early fall. Immunox Multipurpose Fungicide (manufacturer: Spectracide) and Disease Control for Roses, Flowers and Shrubs (manufacturer: Bayer) have a broad label for control of rusts on ornamental shrubs and both are systemic fungicides. Follow label directions and precautions. Controlling the disease on nearby rosaceous hosts may also help reduce disease incidence on Juniperus species, or it may be best to replace the trees with Arborvitae, which is not susceptible to this disease. It is hard to predict how severely the trunk cankers shown in the pictures will affect the overall health of the tree. Sometimes significant cankering can be present without causing significant dieback in the tree.

- so based on the lab's recommendations, you probably would not want to build the patio around the tree.