Rules regarding Themes/templates?

Is it allowable to replace the banner or header graphic that came with the different themes?

You can do whatever you’d like with your WordPress theme. But, before starting, you may want to brush up on a few pointers.
http://codex.wordpress.org/Blog_Design_and_Layout

I cannot find “New World” listed on any of the Theme lists, nor can I find it listed on these forums. Where have you seen it?
http://codex.wordpress.org/Using_Themes#Get_New_Themes

I can’t find any MT Template to WP Theme tutorials, but none-the-less, you may want to read through these for some helpful tips: http://codex.wordpress.org/Importing_from_other_blogging_software#Importing_from_Movable_Type