Yes. A quarter is a period of time and one might say during the week or during the day, so during the quarter is just as correct.
Saying, "I am annoyed of the way you behave.", is grammatically correct.
no
The correct way form of this is "To love is to endure"
If you take out the hyphen, yes. It may not be the right word but this is not a question of grammar. Americans tend to use 'one fourth', and British people tend to use 'a quarter', but really it's a matter of personal preference.
Yes, saying "tomorrow is Tuesday" is grammatically correct as it follows the standard structure of subject (tomorrow) + verb (is) + object (Tuesday).
It can be, like in the following sentence. There were many firsts in this historic week.
Certainly. If one were to make a comparison saying "He can run as quick as a cheetah" then it would be grammatically correct.
No, it's having a meeting or attending a meeting (or you might be holding a meeting if you're the boss).
No. Since "circumspect" is an adjective, "I appreciate your circumspect" is about as grammatically correct as "I appreciate your clean". Saying "I appreciate your circumspect behavior" is correct, similar to "I appreciate your clean appearance".
Both are grammatically correct.
No, it is not grammatically correct to say, 'revert back to'. You would simply say 'revert', as in 'Can we revert to the previous subject?' Revert means to go back (to something), so saying 'revert back to' is saying the same thing twice, which is called tautology.
No, the sentence "You are prejudice" is not grammatically correct. Prejudice is a noun, and you is a pronoun. The sentence essentially is saying that "you" are something that you can not possibly be - the noun prejudice. To make the point you're trying to make, you need an adjective to follow the verb "are." Prejudiced is the descriptive adjective form of prejudice, so the grammatically correct sentence should be "You are prejudiced."