I won't release my software source code, and it will be a commercial application. Can I use the MySQL without paying any fee to MySQL? if it is illegal, any alternative database suggest?
Yes, and you don't have to release your project's source (but you do have to release any modification you make to MySQL itself (only those not the whole program) if you also release your project in binary form containing the modified MySQL code)
In more simple terms, if you modify MySQL and those modifications end up being distributed in binary form you have to publicly release the aforementioned modifications.