Hey Tomas, The fare for travelling form Gangtok to Nathula pass you would have to pay from 400 to 1000 in a shared can depending on the season you are going. ... If you wanna go all alone in a cab then you have to pay more than 4000 rupees .... Go through this link for further details:- https://www.darjeeling-tourism.com/darj_00010b.htm Happy Travelling Bro!!!
Maybe, due to snowfall fall sometime permit the cell to reject the permit to visit Nathula, so keep tentatively scheduled itinerary so you can alternative day in your hand to make it happen especially Nathula. and there is a New year camping eve celebration going so you can club your itinerary accordingly.
And if you're in a group then taxi charges approx.300 pp.