Welcome to the forum Heath10.
I read your post yesterday and was waiting to see what replies you get, not knowing myself a real specific answer to your question.
The thing about trees around a dam, there probably are not any absolute rules. Hopefully some of the experts that have dealt with this for many years have some established guidelines though.
There are people on the forum that have in the past indicated they liked the trees so much for their benefit that they were willing to take somewhat of a chance on them causing problems by having them closer than what would be normally recomended.
Thing about tree roots in a dam, they are less likely to cause a problem while the tree is living than after the tree dies. When a tree dies the dead root will eventually rot out and leave a channel for water to flow. That is the biggest danger. I have seen lots of trees directly growing on a pond dam without the dam leaking so it is not an absolute that they will cause any immediate problem. It is just that they increase the risk of causing leaks. Particularly when the trees die but they could also potentially cause a path even when alive.
So far I have not really given you the answer you want, mostly because I do not have a definitive answer. But I nearly always have an opinion, right or wrong.
So now for my possibly right or wrong opinion. If you had trees directly growing on the dam, I would say that would be a definite negative. Not an absolute "they are going to cause a leak" problem, but definitely increasing the possibility down the road as the trees age. But from your pictures you do not have any trees directly on the dam. That is a positive.
I would say that you are in pretty good shape. I do not know enough about tree varieties to know the rooting structure other than I do know some trees tend to more have a tap root with a root ball contained mostly within the drip line of the limbs. Other trees (like Osage Orange) can extend roots far beyond the drip line and in my opinion would create more of a hazard to a dam if they were close to the base of the dam as in your pictures.
So my personal opinion is, if you value the trees, I would say you would not have any great danger of them causing problems and if they did it would likely be a half lifetime away, based on their location. If you want to be absolutely 100% positive trees can never cause any dam leakage problems, make the area look like a barren prairie.
How's that for hedging my recommendation?