In one of those, I would argue that the MLA style is wrong. Question four was a painfully long sentence. They suggest using a semicolon before the coordinating conjunction. Nope. The sentence overused commas where em dashes are more appropriate. They considered this to be correct:
Although Shelly wanted to go hiking, biking, and swimming on her vacation, she thought she wouldn’t have time for all three activities, since she was only taking a few days off; but, to her surprise, she managed to fit everything in.
If I had read a sentence like that in a book, I would have set the book on fire long before I got to the point of seeing whether the author used a comma or a semicolon before the coordinating conjunction. So for question 4, the correct answer is "neither".
The problem with their use of semicolon is that "but, to her surprise" is not really related to "she was only taking a few days off", making a semicolon joining inappropriate. The author wasn't trying to say, "She was only taking a few days off, but to her surprise, she managed to fit everything in." Rather, what was actually meant was that "She thought she wouldn't have time for all three activities, but, to her surprise, she managed to fit everything in." The "she was only taking a few days off" was basically a parenthetical assigning a reason for why she thought she wouldn't have enough time.
A much better punctuation is this:
Although Shelly wanted to go hiking, biking, and swimming on her vacation, she thought she wouldn’t have time for all three activities — she was only taking a few days off — but, to her surprise, she managed to fit everything in.
By using em dashes (or parentheses if you prefer) to set off a parenthetical clause instead of commas, the sentence becomes eminently more readable/parseable.
So no semicolons before coordinating conjunctions, please. If you ever get to the point where you're about to add a semicolon before a coordinating conjunction because the first part of the sentence is too long or complex, the first part of the sentence is too long or complex. Find another way to say it.
For example, I would suggest reordering it, dropping the "although", and splitting it into multiple sentences:
Shelly wanted to go hiking, biking, and swimming on her vacation. She was only taking a few days off, so she thought she wouldn't have time for all three activities, but, to her surprise, she managed to fit everything in.
And boom. You've just taken a sentence that is painful to read and turned it into a third-grade-reading-level sentence.
But that's just my opinion; it's not the first time I've disagreed with MLA on things, and I'm sure it won't be the last.