Nicole run, runs, running, are running three miles every morning
what's the right answer

Nicole runs three miles every morning.
Present simple because it describes an everyday action, a routine, a habit. Ending in -s because it's the third person in singular.

Why the others are wrong:
-Nicole run would be incorrect (third person has to end in -s for the present simple).
-Nicole running is incorrect, it'd have to be "is running" but that doesn't work for this sentence (if it was "right now" instead of "every morning" the present continuous would be correct, but it isn't the case).
-Nicole are running is incorrect because the third person in singular requires "is", not "are".

Happy new year to you too!