What are signs of the three marks of existence? What are some signs that one might be seeing the three characteristics with more clarity or depth? What might represent that one is having a new and more profound experience of impermanence, dukkha or not-self during one's practice or during any time?

Here are some examples of what is  meant by sign:


When we finish sweeping the floor, that might be a sign of impermanence. 
If an annoying song keeps repeating in the mind that we can't control then that might be a sign of not-self.
We strongly misidentify the body as the self. If while meditating we see past the concept of the body then we might strangely feel like we have no body at some point. This no body effect might be a sign of not-self.
Sweeping is a process made up of many experiences. An experience is made up of the five aggregates. Each of the five aggregates is Anicca, Dukkha, Anatta in nature. That makes each experience Anicca, Dukkha, Anatta. It's not about waiting for something to finish and calling it impermanent. That's obvious even without meditation. That is not strong enough to cut off craving or loosen your grip on conditioned phenomena. You have to develop Sati(awareness) through meditation until you can see these 3 characteristics here and now with each experience(moment to moment). 

Yes, not able to stop unpleasant experiences or not able to prolong pleasant experiences is a sign of Anatta. Then again, reasoning it out like that is not what is expected from Vipassana. You have to be able see it then and there. You have to be able to note that each experience is born due to causes, not because there's a self in them or not because they belong to a self.

Feeling that there is a body or feeling that there is no body are both Anatta. Because both are mere feelings born of causes. Nothing more.