You certainly don't need the multivitamin and it sure can interfere with the fast. It is adding nutrients to your body and probably lactose or whatever it is based in. The body is incredibly efficient at what it does while fasting and any interference isn't usually productive. It should only be done when absolutely necessary and vitamins certainly are not.
You can go as long as you have the strength or motivation to last, it doesn't matter that it is your first time. 10 days is not considered a long term fast in any case and is fine. Just so long as you know how to break it properly and you do so there should be no concerns at all, only weight loss and better health to look forward to! :)