Gangtok & Darjeeling trip

I am visiting Gangtok and Darjeeling from 17 Sept to 22 Sept I need help regarding the below 1.I will be arriving in Bagdogra airport so is there cab facility in or around airport to reach gangtok and how much would it cost? 2.How will be the weather (in terms of rains)? 3.I am planning to go to Nathu la on second day of my trip so do I need a permit two days in advance?
Thanks in advance