Learn English – Why is this sentence incorrect? Why is this other sentence correct

The answer to this GMAT question was not what I expected it to be.

Link to the forum page here.
Up until now, I was certain about two fundamental truths about grammar.

1. It is always possible to connect an independent clause to another independent clause by using an appropriate coordinating conjunction and adding a comma.
2. A list of two items should not have a comma between the two items unless absolutely necessary to avoid confusion.

Now that I have seen this question, I am stumped.
I thought the correct answer was A, but it turns out that the official answer was E. I believe A is correct and E is incorrect.
The reasons cited for A being incorrect and E being correct are the same: parallelism. A does not maintain parallelism between "listening" and "he prayed", while E maintains parallelism between "listening" and "praying". Given that this question and the official answer were supplied by an official GMAT test organization, I am inclined to believe this. But I do not find this explanation satisfactory.

It is to my understanding that you can always combine two independent clauses by using an appropriate coordinating conjunction and adding a comma.

She waved goodbye. He waved back.

We are free to combine the sentences like this.

She waved goodbye, and he waved back.

Back to the original question.

The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier. He prayed for salvation.

Here we have two independent clauses. The first independent clause ("The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier") uses a sentence structure that I have seen many times before where a present tense verb is used even while the main verb is in past tense to indicate that the two are happening at the same time. (For example, "He walked to the park, whistling all along the way.") For this reason, I do not doubt that it is a grammatically correct independent clause. I know the second sentence is a grammatically correct independent clause for obvious reasons.
Given that the two are independent clauses, and that the conjunction "and" is appropriate, we can combine them using the conjunction and a comma. Right?

The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier, and he prayed for salvation.

This gives us option A, which is apparently incorrect. But I do not understand why. The explanation cited for why answer A is incorrect is because of parallelism, but to my knowledge, parallelism does not apply here. We are only combining sentences using the most fundamental method of combining sentences: a coordinating conjunction and a comma. Parallelism is (again, to my knowledge) only applicable when you are creating a list. We would only be creating a list if there was not a comma before the "and".

The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier and he prayed for salvation.

If we remove the comma, we are creating a list and thus have to maintain parallelism.

The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier and praying for salvation.

This ALMOST gives us answer E, but in answer E there is an extra comma.

The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier, and praying for salvation.

Not only do I believe this sentence is incorrect because "Praying for salvation" is not an independent clause (and thus cannot be combined to another independent clause by using a conjunction and a comma), I also believe it is incorrect because you should not put a comma between the items in a list that only contains two items.

I believe this sentence is already obviously incorrect, but it will be more clear if we shorten it a little (but still keep the list of two items).

The dying old priest lay in his bed, listening to his disciples, and praying for salvation.

This appears to be incorrect for the same reason that we would never say

The girls were skipping, and hopping.

or

I went to the store and got milk, and eggs.

So I have multiple questions arising from this dilemma:

1) Does parallelism need to be followed if you are not creating a list and are only combining two independent clauses with a conjunction and a comma?

2) Is my assumption that the creation of a list depends on the presence of commas? (If there is no comma in "The dying old priest lay in his bed, listening to his disciples recite sermons he wrote years earlier and he prayed for salvation," we create a list and thus have to maintain parallelism. If there is a comma, we are not creating a list and can ignore parallelism.)

3) Is my fundamental truth of "It is always possible to connect an independent clause to another independent clause by using an appropriate coordinating conjunction and adding a comma" correct?

4) Is my fundamental truth of "A list of two items should not have a comma between the two items unless absolutely necessary to avoid confusion" correct?