I'm not sure where the email template is, but there will be one hidden somewhere on the site. You say you only want to invite a couple of people, well the site is set up to work as Invite only or anyone can join, not both. The best thing to do is invite them via your normal email and give them the link to the site and possibly the join form. Modzzz has a module for this as well and it may be more flexible. I've actually purchased his module, but haven't tried it yet so I can't comment.
Removing the Captcha is easy, but you may end up being flooded with spammers. If you want to remove it because you don't have a Recaptcha API code, consider replacing it with the Friday Captcha. Oddly I was about to write a tutorial for the Friday Captcha tonight, but you beat me to it. I'll post it here when it's finished.
To remove the Captcha:
1. Go to admin/builders/Profile Fields/Fields Builder The Join Form is usually the first form listed and it's on the left. The Captcha block is on the bottom of column 2.
2. Drag the item to Inactive Items below. (See screenshot)
All done!