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Actually, the acorns that fall from oak trees (as well as those "planted" by squirrels) will cause tree sprouts to pop up throughout the lawn. This article should be of some help in dealing with them: https://www.gardeningknowhow.com/ornamental/trees/tgen/weed-trees.htm

Trees tend to sucker when they are under stress. Lack of water is the most common reason for this, but there can be others. Some trees, like grafted trees, are always under a little stress and will always put out some suckers. You can reduce the number of suckers a tree puts out be removing stress from the tree. Make sure it is well watered and fed and that there are no pests affecting the tree.

If you are still seeing "sap", then it is not sap. It is honeydew and the tree has a pest infestation (likely aphids). It needs to be treated with a pesticide, preferably a systemic one like neem oil. That should clear up the situation.

It is very hard to diagnose tree issues without examining the tree. So, I would recommend hiring a tree expert in your area to look at the tree.

That being said, I know that this is not always possible. It sounds like it is some kind of fungus affecting the tree, but there is also a possibility that it could be a pest. If you treat the tree with both a fungicide and a pesticide, you will treat about 75% of what may be affecting your tree.

Also make sure to practice good tree hygiene and remove and destroy any dead branches and fallen leaves from now through the end of the fall. Pests and fungus can hide on dead leaves and reinfect the tree the following year if they are left at the base of the tree.

its lacking water.....oak trees drink lots of water.as a young tree try a soaker house around ur tree.give it at least half to 1 in watering.a wk.....hot weather more water.

Nearly all insecticides have little effect on Spidermites. You have to buy a true Mitacide to get to them, check at your local garden center or nursery and see what they have available. Be sure to tell them it is to get rid or Mites. There are some systemics on the market that are very good at getting rid of pests. You put it around the base of the tree out by the drip line, working it into the soil well. Then water well. As it goes up through the root system and into the tree, it will kill what is feeding on the tree or causing problems. Spraying the tree and using a systemic may be in order if it is under heavy attack since the systemics can take a while to work.