I have completed two-third of the tasks.

(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.

The phrase "many a" is an idiomatic expression in English grammar. Despite indicating a large number, it is always followed by a singular countable noun and requires a singular verb. This structure emphasizes the individual nature of each item within the large group.

The grammatical rule is: Many a + singular noun + singular verb.

In the original sentence, "Many a person have supported him," the singular noun "person" is correctly used after "many a," but the verb "have" is plural. To ensure grammatical agreement, the plural verb "have" must be corrected to the singular verb "has."

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'.