can’t download new theme

The program keeps asking for hostname, username and password. Does the program require my mysql info or wordpress info?

No. It is just asking for your hostname, ftp user name and password, because it is acting on your behalf to automatically download and install a theme via ftp. In essence, it (the automated installer) is pretending to be you. However, it still needs your hostname info, ftp login info and password to perform the requested action.