My question is: am I allowed to remove the links in the button of my forum, and replace them with an actually sentence that still gives credits to both Phpbb and forumotion? I know you are allowed to do that with HTML pages but I just wanted to double check before I actually do it on the entire forum. Cheers.

You are not allowed to change or remove them with any code.  You can use credits to remove them, but only the Forumotion links will be removed.  The others that stay after using credits can not be removed at all.