MySql security

Hi, Since i dont know any mysql group, i will try here - it is anyway related to php. When i want to make php/mysql application i have mysql on the server and i connect to it with mysql_pconnect("localhost","root","") and it works. I assume that any user or hacker could connect to mysql database like this. So, i want to create my database and i want to limit access to this database for some usernames and passwords. I know MSSQL or Interbase can do it - but how i do this in mysql. If this is offtopic can someone point me to any mysql newsgroup. Other question is: if i need to make application which uses credit cards, how can i increase security for it. I have heard about https protocol, but dont know much about it. Any link would be appreciated. Thanks, Radovan