Hi Anne,
Not a problem - these things are important to check!
Yes, you will be able to activate/validate your Japan Rail Pass at Narita when you arrive on Thursday provided you reach the validation office during it's opening hours. At Narita, the hours of the JR counters are:
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T1 Travel Service Center: 8:15-19:00
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T1 Ticket Office 6:30-8:15, 19:00-21:45
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T2 Travel Service Center 9:30-20:00
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T2 Ticket Office 6:30-9:30, 20:00-21:45
(T1/T2 = Terminal 1/2)
When you activate it you will be able to specify the starting date to be Sunday the 27th of May for your trip to Nikko.
The Japan Rail Pass validity is in full days, so looking at the calendar a 14 day rail pass starting on the 27th May will be valid for 2 full weeks with the last day of validity on Saturday the 9th of June. This means that yes, you will be able to use it for your journey back to Narita.
Hope this helps put your mind at rest! Have a great trip!