Many a person have supported him.

(Correct the sentence)

The word "information" is an uncountable noun in English. This means it does not have a plural form ending in "-s" or "-es" and should always be treated as singular. Therefore, "informations" is grammatically incorrect.

When you want to refer to individual items or quantities of "information," you should use phrases like "a piece of information," "much information," "a lot of information," or "some information." For example:

    
• Incorrect: "She gave me many informations."
    
• Correct: "She gave me much information."
    
• Correct: "She gave me a lot of information."
    
• Correct: "She gave me several pieces of information."

In the given sentence, simply removing the "s" from "informations" makes it grammatically correct: "I need some information on the issue."

While the original sentence "Please open page 20 of the book" is grammatically understandable, the verb "turn to" is conventionally and more idiomatically used when instructing someone to find a specific page within a book. The verb "open" typically refers to the act of initiating access to the book itself (e.g., "Please open the book"), or to a specific page when followed by "to" (e.g., "Open the book to page 20").

The phrase "turn to page X" directly conveys the action of navigating to and locating a particular page. This usage is standard in educational and instructional contexts.

I have completed two-thirds of the tasks.

The error in the original sentence, "I have completed two-third of the tasks," lies in the formation of the fraction. When expressing fractions in English, the following rules apply:

    
• If the numerator (the top number) is one, the denominator (the bottom number) remains in its singular form. For example, "one-third," "one-fourth," "one-fifth."
    
• If the numerator is greater than one, the denominator takes on a plural form. For example, "two-thirds," "three-fourths," "four-fifths."

In the given sentence, the numerator is "two," which is greater than one. Therefore, the denominator "third" must be pluralized to "thirds." The correct sentence is "I have completed two-thirds of the tasks."

Don't mind waiting outside.

The verb 'mind' is typically followed by a gerund (the -ing form of a verb), not an infinitive (to + verb). In the given sentence, 'to keep waiting' is an infinitive phrase, which is grammatically incorrect after 'mind'.

The correct structure requires a gerund after 'mind'. Therefore, 'to keep waiting' should be replaced with the gerund 'waiting' to form the correct idiomatic expression 'mind waiting'.