Hi Mojave,
1) 이해하는 데 어려움을 겪고 있어요.
2) 이해하는 데 어려움이 있어요.
-> Those two mean the same and I would say you can use them interchangeably.
But IF I will have to point out the difference between them, 1) sounds like "I am having a difficulty understanding (because my ability is not good enough)." and 2) sounds like "I am having a difficulty understanding (because the thing I am trying to understand is not clear enough)".
3) 이해하지 않아요.
-> "I do not understand (on purpose)" -> If you say this, it sounds you are a cold-hearted or mean person.
4) 이해되지 않아요(=이해 안되요, 이해 못하겠어요).
-> "I do not understand = I cannot understand"
Hope it helps,