I am beginner for MySql, Apache and PHP. I am not sure to use MySQL to create the database which will be compatible using with Apache and PHP code. will there be any problem? what about MS SQL server or SQL plus?

Use Apache with MYSQL. I just installed a LAMP system four weeks ago and I am enjoying it thoroughly.

i will create search engine for children information on the web-based. i'll use MySQL as database, and PHP to code for retrieving the information from database to web-based interface.
do i need to write the syntax of mySQL to connect with the Apache server? if yes, how i am going to do that?

u don't have to write special synatx , and have no worries about mysql , The whole google is on mysql .

Thank you for all helps.. i really appreciate it.
is there a free download MySQL GUI window? what websites?

Check this thread

http://www.dbforums.com/t1002154.html