What is PHP core?

1-What is PHP core?
2-How does it work?
3-What is Zend engine?
4-Which language is used to build PHP core(For PHP 5) and zend engine?
5-What is relationship between C and PHP 5?

Sounds like you’re trying to get us to do your homework.

with all due respect, You are wrong!~

I research about buffer overflow in PHP.

If PHP core is written by PHP C, Then it is vulnerable to Buffer overflow.

I want to know relation between C and PHP.

By that logic, everything is vulnerable to buffer overflow attacks. Read about suhosin, I think I posted that link on one of your topics but it seems you neglected it.
Also, if you’re researching about buffer overflow in PHP - it’s still better and faster to google the answer than getting biased opinions on one of many forums out there.

Ever heard of a search engine? Google maybe?

Sounds like you’re trying to get us to do your homework.

PHP Core works by being in the core of Earth?

It took me exactly 20 seconds to google out all of your questions, despite knowing some of the answers beforehand. I really don’t understand what your concerns are and why you find it difficult to find answers on your own. In the end, PHP is open-source, you can always look at its code and find out for yourself, given the fact you actually understand C.
Seems to me that you actually are asking bunch of other guys to do your homework.

How does PHP core work?

the PHP engine is written in C. That’s the relation. The answer to that was in the information you copy/pasted in that thread you linked.
Try reading your own posts?