A couple
When a couple means simply two and refers to two non-animate entities, it combines with the plural form of the third person present tense:
A couple of places are said to be haunted at the university.
A couple of houses are turned into little museums.
A couple of cars are parked outside.
Although the noun itself is in the singular, what it really describes is more than just one thing or person. It doesn’t matter whether you mean literally a couple, i.e. just two people or things, or you use “a couple of” synonymously to “a few”; it represents a plural idea, so the correct form is:
There were just a couple of people at the party. (correct)
There was just a couple of people at the party. (wrong)
Only when “a couple” is not followed by “of” and is used to mean “a pair of people”, and you refer to the couple as a whole, not just to individual persons who constitute it, you should treat it as being singular:
A couple in love is always a nice thing to see. (correct)
A couple in love are always a nice thing to see. (wrong)
A couple is seen through a shop-window near Via Condotti.
When a couple is feeling stressed, humor can be an effective way of breaking through the tension.
A young couple is living together but not married.
Unless one wishes to emphasize the separateness of each partner:
This makes a one-on-one relationship difficult when a couple are 8000 miles apart..
How a couple are taxed in the year in which they separate will depend on how they were taxed as a married couple.
More than one
When a noun phrase contains more than one and a singular noun, the verb is normally singular:
There is more than one way to skin a cat. More than one editor is working on that project. More than one field has been planted with oats.
When more than one is followed by of and a plural noun, the verb is plural:
More than one of the paintings were stolen. More than one of the cottages are for sale.
When more than one stands alone, it usually takes a singular verb, but it may take a plural verb if the notion of multiplicity predominates:
The operating rooms are all in good order. More than one is (or are) equipped with the latest imaging technology.
Q: Which is better: “More than one person is going” or “More than one person are going”? Put more abstractly, should the verb agree with the meaning of the word “one” or the meaning of the phrase “more than one”?
A: The phrase “more than one” can be either singular or plural, depending on how it’s used, according to The American Heritage Book of English Usage.
When “more than one” modifies a singular noun, it goes with a singular verb: “More than one person is going.”
But when it’s followed by “of” and a plural noun, it takes a plural verb:
“More than one of the people are going.”
When “more than one” stands alone, it can be either singular or plural, depending on whether you want to emphasize the oneness or the more-than-oneness.
If someone asks you how many people are going, for example, you could reply “More than one is too many” or “More than one are going.”
The rest
"Rest" is one of the words that functions as a partial of a whole. Others in that class are fractions, percentages, and the words some, any, none, part, remainder, etc. These words create a significant exception to the rule that prepositional phrases have no effect on subject-verb agreement.
The verb is determined by the object of the preposition. And it can change.
The rest of the cake was missing.
The rest of the cakes were missing.
The rest of the students were absent.
The rest of the student was found in another dumpsite.
The first question was easy, but the rest were very difficult.
Majority
https://brians.wsu.edu/2016/05/24/majority-are-majority-is/ - nice solution
дебаты - https://forum.wordreference.com/threads/collective-nouns-the-majority-is-are.36923/
https://languagetips.wordpress.com/2011/07/07/weekly-language-usage-tips-the-great-majority-is-or-are-collective-nouns-uncomparable-or-absolute-adjectives/
‘ Majority’ is a collective noun that can take either a plural or singular verb depending on the context. If it refers to individual items or people acting individually, it requires a plural verb.
The majority are going to prepare either desserts or appetizers.
Since they are preparing different courses, it is apparent that the people here are acting as individuals and not as a unit.
When acting as a group, a singular verb is needed.
The majority supports the new legislation.
Here, we don’t have any information to differentiate the supporters, so we treat them as a collective unit and use a singular verb.
In the example provided by the reader, the phrase, ‘the majority of those surveyed’ provides the clue: those people were surveyed and answered the questions individually, so a plural verb is needed.
A great majority of those surveyed drive or ride a bus rather than walk.