Q.Can Pine Trees “Infect” a Green Euryops?
Last year we had transplanted a green euryops and it was placed under a type of pine tree. It was doing well until now. I have noticed a type of white “crystallized” substance on the leaves, and so the plant flowers have small blackness (like lots of small bugs) on them, so they will not open fully. Almost like maybe a mold? Could the pine tree dropping sap or such over the winter time hurt the plant and, if I move, can it recover?

The first thing to do is to move your plant - it needs full sun, and growing under the shade of a tree is going to weaken it and leave it open to attack from various bugs and disease. Read this article about bush daisies: https://www.gardeningknowhow.com/ornamental/shrubs/african-bush-daisy/growing-bush-daisies.htm.
You can take some samples of leaves and flowers to the Extension Service to find out the best treatment for the attackers, also the names of good plants to use beneath the pine. This link will help you locate the nearest service office: https://www.gardeningknowhow.com/extension-search/