I am doing my best to try and incorporate the gallery into my personal website, but I keep getting a bunch of errors.
First of which it says I'm running 4.4.9 PHP when I need at least 5.0;
what does that mean?
And second, I keep getting this:
"Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)"
and
"Fill in the information below and setup will attempt to update your zp-config.php file."

How do I remedy ANY of this?!?

1. What the message says, the PHP version on your server is not sufficient...So you need to either switch the PHP version or upgrade your webspace. Since you seem not to be that knowledgable about web stuff, ask your host.

2. You did not enter the MySQL credentials in the form indicated so Zenphoto could not connect to the MySQL server. Again ask your host for these credentials.

I really recommend to learn at least what PHP and MySQL means before trying to install an application on your server.