Linux is a whole new ball game, unlike windows, Linux is secure by default. I see a few issues in the log, you biggest one is, you haven't set up your MySql accounts properly.
See if your distro includes 'mysql-administrator', if so, install it. If not, go here;
http://rpm.pbone.net/ try to find and install it. This program (mysql-administrator) will make things very easy for you.