I used MAMP about a year ago when I first started learning WP with Shoutbox. I had a few issues too at the beginning but I haven't used it for ages so it's a bit of a blur. Some of the things I do remember were:
1. Install MAMP and WP properly. I used this video to help: http://www.youtube.com/watch?v=10fbwScPMtQ
2. I remember I had an issue with the permissions in the MAMP control panel. Click HOSTS (not SERVER) and you will see the 'permissions' button in the General options. You have to manually set them so you have permissions to do everything (check all the little check boxes and save it). This might be what is causing you problems.
3. Make sure there is enough memory allocated to the php in MAMP and later when you go online. It can cause problems with the Template Builder if it is too small. I think the default is 16 or 32mb. I pushed mine up to 64mb or more. You change it by editing the php.ini file for the version of php you are using from: top menu /File / Edit Template / PHP.
I changed these settings I think:
memory_limit = 64M ; Maximum amount of memory a script may consume (64MB)
post_max_size = 64M ; Maximum size of POST data that PHP will accept.
upload_max_filesize = 64M ; Maximum allowed size for uploaded files.
Your database looks a bit small. Did you install the Shoutbox default template with the test images and test posts? I think the default phpmyadmin database should have about 24 tables.
As Devin says, it's a bit of a bugger to assist online because we can't see what you have on the computer. Try some of these things (the permissions for example) and let us know what happens.