Hi, Priya. There's a lot of depth to your inquiry, so please pardon the injustice I am about to do with my short reply.
2. Absolutely. Eat your own dog food, IMO.
3. Your security considerations for the platform will transcend API architecture. But to the breadth your question, it might be really useful to read this article (and read all of the many links!) to get some pro/con lists
http://www.thebuzzmedia.com/designing-a-secure-rest-api-without-oauth-authentication/ Despite the tone of the article, there's a lot there to guide you in addition to what the rest of the group here will more specifically contribute.
(Told you it would be short.)