On being a half-indian in India

I'm not exactly sure how many times in the last couple days local Indians will talk to me and mention somewhere in the conversation how I look Indian, but do not sound or act Indian. Firstly, this is a big win as I tanned up and am sporting a nice travel beard with the hopes of fitting in better. Secondly it makes me feel really odd, for several reasons, some of which I'm sure I haven't figured out yet. In Canada I usually would get people being a little confused or unsure of what my genetic background was as there were many awkwardly initiated conversations with people wondering, essentially, why I look the way I do (which I suppose isn't really clear-cut defined in any standard race category..if I can put it like that). In Canada I'd hear things like "So what are you?" or "what nationality are you?". Again, sometimes it came out horribly awkward as some people just couldn't quite figure out exactly how to ask the question. The answer, if you were always wondering but never asked is as follows:

Nationality - I'm Canadian (although I have dual citizenship with the UK)
Genetic Makeup - My mom is Indian, from Bombay, and my dad is British. She's 100% dark-skinned, and my dad is 100% fair skinned. The way it seems to make the most sense to me is that I got more of my skin tone from my mother, and got more of the body tone from my father. I didn't, unfortunately, get his blue eyes however.

In Canada people seem interested because they couldn't figure it out, it was a puzzle, a mystery. In India, they can see I look Indian, but the puzzle is more of the cultural background. They want to know "Do you speak Hindi?", "Where is your mom from?", "Do you like Indian food?", "What do you think of India?". On some level I almost feel like an alien look-alike. Maybe a good analogy is the movie Avatar, where the soldier gets put in the native body, but doesn't really know much about the culture or the language. On some level I fit in, at least until I open my mouth. People seem to be comfortable around me as if I can bridge some gap across some ongoing curiosities they have between their world and that of the west. I guess it's just weird to me because my perspective is always to define myself through my culture and experience in the west. I grew up completely in a westernized culture and didn't really stop too many times in the mirror to think about how well I looked the part. I guess it opens up more questions than provides any answers. How much do people define me by the way I look? What about the way I speak and act? How much of us is seen, and how much is heard? And at the end of the day, do people really connect with us the way we think they do, or did we have it backwards the whole time?