Since “whenever” is a subordinating conjunction linking a dependent and independent clause, no comma is needed before it. Commas are required before coordinating conjunctions, but not subordinating conjunctions.

This question is checking for understanding of the subordinate conjunction "provided that." If it helps, "provided that" can be thought of as equivalent to "on the condition that." The only error in the sentence is that "provided by" is used instead of "provided that." "Provided by" has a different use (as a regular verb) and is not a subordinate conjunction. 

An example of "provided by" used correctly: "Her cell phone service was provided by her local cell phone company."

An example of "provided that" used correctly: "Provided that she was paid overtime, Kara agreed to clean the golf course before she left for the day."

In the sentence above, the words "when" and "whenever" are being used to cause the second portion of the sentence to be a subordinate clause: they are subordinate conjunctions. They also mean roughly the same thing, so using both is redundant. One of the conjunctions should remain in the sentence, and the other should be deleted. The best way to correct the sentence above is:

"When we had enough to eat when I was younger, my whole family was completely overjoyed."

OR

"Whenever we had enough to eat when I was younger, my whole family was completely overjoyed."

In the sentence above, the words "but" and "yet" are being as subordinate conjunctions. They also mean roughly the same thing. Only one of them is necessary, and the other should be deleted. The best way to correct the sentence above is:

There's an old saying, "great men are rarely good men," yet many of my favorite heroes from history were exceedingly kind.

OR

There's an old saying, "great men are rarely good men," but many of my favorite heroes from history were exceedingly kind.

In the sentence above, the word "when" is being used as a subordinate conjunction. Any such subordinate clause must be separated from the rest of the sentence by a comma. The best way to correct the sentence above is:

"When I was a young man, I used to love to go out and hang out in parks."

The word “between,” relating two independent clauses, implies that the correct conjunction to be used here is “and” rather than “or.” 

The verb “prefer” takes the preposition “to,” not “than.” In other words, it is grammatically correct to say families prefer “suburbs to cities” but not correct to say they prefer “suburbs more than cities.”

This sentence begins with the restrictive clause, “Many endangered species.” Using the word “which” after a restrictive clause is incorrect. Rather, we must use the word “that.”  While it is a common grammatical error to use "that" in situations when "which" is needed, it is equally incorrect to use "which" in instances when "that" is required, like after a restrictive clause. 

"Home" contains the error in this sentence because parallel sentence structure dictates that each part in a series must use the same type of word and employ the same tense, if the words are verbs. In this case, the first two parts in the series are prepositional phrases ("to the park" and "to the store"), but the third part is a noun "home." Because only part of one of the prepositional phrases is underlined, we can't change them, so we would need to change the noun, "home," to correct the sentence's error.

Given that two of the three verbs in the series are in the present tense ("choose" and "log in"), it follows that "clicked" should also be in the present tense, not the past tense, in order to conform with the rest of the sentence.