In future, it's better to post your question in the same thread as the original question - then we don't have to go back and forth to discuss / see the problem.

"compound" means there's more than 1 of whatever you're talking about and the word "and" is connecting the things.

So:

Amy and Sarah went to the store

"Amy and Sarah" is a compound subject. There are two subjects (Amy, Sarah), and they are connected by the word "and."

Amy swam and skiied.

"swam and skiied" is a compound verb. There are two verbs (swam, skiied), and they are connected by the word "and."

in E, we have ", requiring <doctors to see more patients> and spending <something else>"

or, more simply, ", requiring and spending"

First, "comma -ing" is an adverbial modifier, so ", requiring" is an adverbial modifier. The word "and" indicates parallelism, so "spending" is parallel to "requiring" and is also therefore an adverbial modifier. Now, we have two adverbial modifiers, and they're connected by the word "and" - hence, compound adverbial modifier.

Adverbial modifiers modify the preceding clause, so in E ", requiring..." and "spending..." should each modify "union members are less likely than nonunion members to be enrolled in lower-end insurance plans." So, is the fact that "union members aren't as likely to be enrolled in the lower-end plans" the thing that then requires doctors to see more patients? If not, then this is not the correct construction.