Ideas aren't protectable by copyright or trademark law and unless a "process," not by patent law either. But you're on the right track with an NDA. I haven't reviewed the NDA you downloaded, but the trick is still in defining what is being disclosed and what is subject to the NDA. You may need a lawyer to help you with that. Please see my Legal Guide "How to Protect Your Ideas Without Giving Them Away."
Have you secured the domain names for the website that your idea relates to? Owing those before pitching any propective investors/venture capitalists/web designers is a cheap way to package your idea. Please see my Legal Guide "Domain Name Ownership - Things You Need to Know."
Yes, you should have a written partnership agreement with your friend. Even a good friendship can get stressed by a venture like this, especially when there's money to fight over, and as a practical matter, if there is two of you and so far you're deciding everything by consensus, you should provide for what to do if you need to break a tie.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.