When comparing more than two items, you should use superlative adjectives. So, in this case, you should use the word "best."

Here, because you are making a direct comparison between two things, and the adjective in question is "fun," "more fun" is the correct construction. Additionally, you want to use "than," which indicates comparison, rather than "then," which indicates time or causation. 

Here, you have a comparison between an individual and a group of people the size of which is unknown. Because you are not comparing two things directly, this is a superlative comparison. As such, the correct construction is "most avaricious."

In this sentence, one team's ideas are being compared to the ideas of many teams; therefore, it is correct to use the superlative form of "simple" ("simplest") rather than the comparative form ("simpler"), which is used when comparing two people or things. This means that the correct answer is "this team's proposal was the simplest." "Many" is an excellent warning sign of a superlative to come!

When two things are being compared, it is necessary to use the comparative form of the adjective or adverb in question. In the case of "strong" the comparative construction is "stronger," and it is correct in the sentence. When more than two things ("a few things," for instance) are being compared the superlative is required: "Of all the boys, Tom is the strongest." A superlative is used to distinguish one person or thing from a group, a comparative is used to compare one thing or person to another.

When two things are being compared, it is best to use the comparative form of the adjective or adverb in question. In the case of "quickly" the comparative construction is "more quickly," and it is correct in the sentence. "As quickly as" would also be acceptable in this situation.

When three or more things are being compared, it is best to use the superlative form of the adjective or adverb in question. In the case of "good" the comparative construction is "best," and the example sentence is correct as written. If the speaker were comparing him- or herself to another specific chess player, then the comparative would be needed, e.g. "I am a better chess player than Tom."

When three or more things are being compared, or there is an indefinite comparison (such as one teacher out of a whole school group), it is best to use the superlative form of the adjective or adverb in question. In the case of "bad" the comparative construction is "worst," and it is correct in the sentence. It is reasonable to assume, in this instance, that there are more than one other teacher in the "whole school."

In the above sentence, the narrator is comparing his/her favorite book to all books, ever. Therefore, because three or more things are being compared, the superlative construction must be used. The best way to write this sentence is, "I think that my favorite book is the best book of all time."

When comparing two (and only two) things, one must always use the comparative construction. In this example, two things are being compared: how quickly the narrator has run before, and how quickly he or she is intending to run the day of the meet. As such, the best way to write the sentence is: "The day of the track meet, I was prepared to run more quickly than I ever had before." When one thing is being distinguished from a list of three or more things, a superlative construction is required.