Answer: Some apricot trees are self-fruitful and others do better with a pollinator. It's difficult to tell whether the variety you have needs a pollinator, but if it produced fruit in prior years, there may be an appropriate pollinator in the neighborhood. Because apricots bloom early in the season, they are subject to late frosts. Not only can the flowers be damaged by cold weather, but insect activity is low during cold spells, leading to lack of pollination. Some apricots require a pronounced winter chill before they'll set fruit. If yours is that variety, you may only get fruit after a cold winter and a warm spring. Try to find out which cultivar you have so you can determine whether it needs a pollinator.
Sap is normal for both plum and apricot trees. Sometimes it indicates an injury and other times it simply means that the sap is really running and has escaped through natural openings in the tree. I'm only guessing, but the flat, oval things may be scale insects (if so, just pry them off), or it could be algae or lichen growth (again, just pry it off). Since you've got new growth, I'd say your tree is happy, just unproductive this year. Other than the above, hope for the right weather conditions so you'll have a bumper crop!
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