1. "Tessa heard Paul close the door" 2. "Tessa heard Paul closing the door" They mean the same but they create different images. In #1, Tessa heard something. That's all. It's just a statement of fact. Present participles paint pictures. When you hear someone say "closing the door", it's as if you are watching a video showing the door in motion from an open to a closed position. That makes the present participle especially useful for friendly conversation. While you tell a story to a friend, present participles can create images that make your story colorful. The same applies to your sentences about Jessica. Do you want to state a fact, or do you want people to imagine Jessica crying. To do the latter, use the present participle.

The difference is subtle. If it was important, the speaker would add more details. The difference in verb tense alone doesn't convey a lot of meaning. "Close" means the speaker is thinking of the action as a single unitary event at a single point in time. Tessa didn't pay attention to any details. The door was open. She heard something. She said to herself "The door is closed." It takes several seconds to close a door, and if you pay attention you may notice a series of different sounds. There might be a slight whoosh of air. There might be a squeak from the hinge. There might be a "click" as the bolt hits the plate, and then a "snap" as the bolt slides into place. There might be more sounds Paul locks the door after leaving. If the speaker is thinking of the action as extended in time, they might say "closing." For example, "Tessa heard Paul closING the door, but before it was closED he stopped. He stuck his head back in and called 'I'm going to the supermarket, do you need anything?'" On a subway, you might hear an annoucement, "Please step back, the doors are closing." It wouldn't make sense to say "Please step back, the doors are closed." If the doors are already closed, you don't need to step back.

They are very similar. The "-ing" makes me think that there is an ongoing action. "Closing the door" would mean that she heard the door swing, the metal latch made a sound, and then the heavy sound of the weight of the door hitting the door frame, are several sounds. Hearing the closing of a door is listening to more than one thing. It also took a few seconds to happen. If you see someone crying then you observe them over several seconds. They would shake a little, make sounds with their nose, or whine a little. Seeing someone crying would take a little time. You would notice the person's actions.

With "close" the door, Paul closed the door. With "closing the door, maybe Paul closed the door (same meaning as with "close"), or maybe he started closing the door but didn't finish.

Both mean the same, the difference is very subtle and nuanced, "close the door" may possibly imply that Paul closed the door quickly. "closing the door" suggest a slow ongoing action Paul closed the door slowly possibly so has not to wake up Tessa. In story telling or recalling memories and events a native English speaker or writer would add more descriptive adjective details. Such as suddenly quickly loudly for "closed the door." And slowly gently quietly for "closing the door so as not to wake me" spoken written from Tessa's perspective.