OK, for number 1 (having, again read the readme file provided by the plugin): Replace the line <?php echo recaptcha_get_html(); ?>, removing the other one. The default "style" without arguments is the light-colored one, which is the styling you want.

For the "emails not sending", a couple of questions:

1. Did your contact-us emails send before the change?
2. When you click the "send" button from the contact-us page, do you receive a message that the email has been sent?
3. Are there any myDEBUG*.log files present in your store's /logs directory? If so, try to send the contact-us message again and see if one is generated when you do that; post its contents if found.
4. What is the value for your store's Configuration->Email Options->Set "Contact Us" Email Dropdown List?