Learn English – Which is correct: “as good as possible” or “as best as possible”

That's a "trick" question because it is not about what follows "best", but simply about "should you use 'in' or 'on'?".

The double-trick is that in some case, you could (with a slight variation of context) use 'for'!

I'll do my best for the TOEFL preparation so I'll get higher score on the exam.

Anyway, if we stick to the initial choice 'in' or 'on', the final trick is in some case, both could be used, like the two first examples ("on" maybe being more commonly used in the US)

I find (personal rule)

• "in" standing for "during" or "within" (or other similar meanings)
• "on" standing for "about" or "referenced by" (or other similar meanings)

Meaning I don't find your examples "wrong".

Use of 'are in good moods'

Different Google Books searches for "are in good moods" yield different results, depending on time frame chosen and additional words chosen to include with the phrase, but a search specifically for "are in good moods" across the period 1700–2005 turns up only 43 matches. The earliest match I found is from V. S. Srinivasa Sastri, Lectures on the Ramayana, (1961) [combined snippets]:

For we all know from experience that neither the best nor the lowest amongst us, neither men nor women, neither Westerners nor Easterners, none who is human, is able to occupy one level of thought, one level of action, and one level of function; we go up sometimes when we are in good moods, receptive of ethical notions, conscious of our duties, comparatively strong to resist temptations, in noble surroundings, amidst noble people, thinking noble thoughts and capable of doing noble deeds. Alas! such moments are not always available.

Another fairly early instance occurs in a twilight-of-the-USSR offering from Andrei Frelov & Lois Becker Frelov, Against the Odds: A True American-Soviet Love Story (1983) [combined snippets]:

In the Soviet Union people do not smile as often. They buy things of poor quality from the government, and even these inferior items do not exist in quantities sufficient for normal life. Therefore, people are often in a bad temper, and insult one another with no apparent cause. But, at the Central Market in Moscow, where farmers receive good money for the vegetables and other foods that they have raised on their own private parcels of land, the picture is completely different. These people try to satisfy and please their customers. They are in good moods. They are polite, like in America.

Notice the contrast between the fifth sentence ("They are in good moods") and the wording of a comparable construction in the third sentence ("people are often in a bad temper"—rather than, as one might expect from the model of the fifth sentence, "people are often in bad tempers").

Something similar happens in this match from Andrea Henkart & Journey Henkart, Cool Communication: A Mother and Daughter Reveal the Keys to Mutual Understanding Between Parents and Kids (1998):

If something comes up that you really want to do and your parents won't let you do it, try to reason with them by discussing it. The trick is to calmly let them know why something may be so important to you. Usually the best time to explain things is not in the heat of the moment. It is definitely not a good idea to try to work things out during, or even right after, a fight. Whenever you decide to talk to your parents, make sure they are in good moods. They will listen better when they don't have so many other things on their minds. The way to find out if they are in a good mood, and if it is the right time to talk with them, is simply by asking. Remember to keep calm.

Here the author switches from "are in good moods" to the more common "are in a good mood," when the discussion shifts from theoretical and general to hypothetical and specific, suggesting that her commitment to "they are in good moods" is less than a wholehearted.

The great majority of the matches are from 2000 or later, starting with Spencer Rathus, Psychology: The Core (2000):

THE HELPER: WHO HELPS? Many factors affect helping behavior:

1. Empathic observers who are in good moods are more likely to help. Most psychologists focus on the roles of a helper's mood and personality traits. By and large, we are more likely to help others when we are in a good mood (Baron & Byrne, 1997). Perhaps good moods impart a sense of personal power. People who are empathic are also more likely to help people in need (Darley, 1993).

Here, again, "are in good moods" rapidly and unconsciously gives way to "are in a good mood" when the subject shifts from "Empathic observers who" to "we."

Use of 'are in a good mood'

In contrast to the 43 matches it finds for "are in good moods," a Google search over the same period for "are in a good mood" yields 135 matches—meaning that the singular form "a good mood" with are in is about three times as common in the search results as the plural form "good moods" with are in. This form also goes much farther back, with a first occurrence from Robert Wodrow, The History of the Sufferings of the Church of Scotland, from the Restauration to the Revolution, volume 2 (1722):

March 11 [1684]. the Justices and Advocate are in a good Mood. Anent the criminal Process in Dependence, against Sir William Lockhart of Carstairs, Mr. Hugh Maxwel of Dalswintoun, (who, towards the End of this Year, got not so well off) John Campbel of Horsecleugh, James Campbel of Greenock-mains, and about Eighty Country People, who are present, the Advocate declares his Majesty hath ordered the Dirt to be deserted against them ; and the Lords desert it simpliciter.

The same idiomatic form appears almost 300 years later in, for example, Barry Babin & Eric Harris, CB 7 (2015):

As a result, retailers should prefer that consumers shop in their stores when they are in a good mood. Many cues can make a consumer's mood more positive, including music, smells, and even exposure to lucky numbers!

This appears to be, by a significant margin, the more common way of referring to the good mood(s) of multiple people, though "are in good moods" is not exactly rare.

Emergence of 'in a good mood' as a common expression

The rise of "in a good mood" (red line) as a common idiomatic expression is chiefly a twentieth-century phenomenon, as this Ngram chart for the years 1710–2005 reflects:

In contrast the wording "in good moods" (blue line) is far less frequent. The much greater frequency of "in a good mood" may act against any natural inclination to attribute being "in good moods" to multiple individuals that may each be in a different (but good) mood.