Form doesnt save to database

You have small mistake in your code. Use same variables in $data array and storing form data. Change your code to this:

$data = array(
    'name1' => $name,
    'date1' => $date,
    'email1' => $email,
    'phone1' => $phone,
    'message1' => $message
);

You have used $name at one place and $name1 at another place below.