http://www.usingenglish.com/quizzes/

English Language (ESL) Grammar Quizzes for Students - UsingEnglish.com

Reference to the link above, where answers have been given at the end of every quiz.
But I am unable to find the answer WHY of a quiz. Is there any page on this site which can explain the reasons as well?

For example,
Quiz: While & During
We met ___ the Xmas holidays.
during
while
where the answer is 'during'. But why the while? Explanation or logic?

Another example
Quiz: By or Until
I'll keep phoning ____ you pay me.

by
until
Where the answer is 'until'. But why? Logic?

Is there any page of explanation to these quizzes on this site?

No, we have hundreds of quizzes and simply do not have the time to write explanations for every question. However, we do have this forum, where you can ask questions. If you're not sure, ask here.