fitbit questions about logging exercise

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I'm new to fitbit- I'm sure this has been asked but I can't find now

when you use a bike or an elliptical - or if you are swimming ? - does it track anything for you ? steps or calories ?

when I'm done working out - let's say I did 45 min of elliptical - should I log it here on mfp as my cardio exercise - or should I log it into fitbit ?
I don't want it to " double " the calories burned so how do I prevent that ?

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