I doubt it will fix your problem but lose the trailing slash from the base url. It should be http://www.adventurecat2.com/guestbook not http://www.adventurecat2.com/guestbook/. If the problem was with the permissions it would give an error messae unless your hosts are like mine and turned off all PHP error messages, nice people they are.
You can block an entire IP block if you wish, not advisable though. My image verifcation is best way to combat spam or change the name of the name input from gb_name to something else.
You can't. Only options to put your message in the html of the page or to reverse the order entries are shown so that the oldest entries are shown first.
Whats the point in a guestbook if only certain people can post? The clue is in the title, GUESTbook. The only way you could stop just anyone posting is to password protect the addentry.php file.