Could and was able

Hi,
In a book titled "What's So Amazing About Grace" by Philip Yancey, in chapter 8, titled Why forgive, it has this paragraph:

"For a long time, I had felt foolish about forgiving my husband," Rebecca told us. "But that night I realized the fruit of forgiveness. Julianne was right. I could understand what she was going through. And because I had been there too, I could be on her side, instead of her enemy. We both had been betrayed by the same man. Now it was up to me to teach her how to overcome the hatred and revenge and guilt she was feeling."

Q1: For the part "I could understand what she was going through," would you say it was denoting possibility since the modal "could" can't express abilily, past and present and future? If it was denoting possibility, could I replace with the phrase "might" and "may"? I think I should since the words "might" and "may" and "could" mean the same in the sense of their ability to carry the notionn of possibility.

Q2: I think this can't be written like this: Two days ago, I could throw this discus. And I think we have to resort to using the words "was able to," thus: Two days ago, I was able to throw this discus.

Then again, I think we can use the modal to express one-time failure like this: Two days ago, I couldn't throw this discus. For that, I think we can also use the phrase "was able to" too (like this): Two days ago, I wasn't able to throw this discus.