The Date Errors are a php server issue.
The host should be able to update the php.ini file for you to set the default timezone to prevent that error from occurring. It happens if the default time zone is not set in the php.ini.
Alternatively, Try adding the following to your page...
The list of valid timezones is here...
The failure for sending the email is most likely an issue wit the from address, try changing that address, it may be that the SMTP server has blacklisted that address for some reason.