No. Sikkim is a part of North East India and owing to the same ecological similarity and close proximity to the Sister States, Sikkim is called the 8th "Brother".
Sikkim recently inaugurated an airport in Pakyong near Gangtok, which will be running regular flights to & from Sikkim very soon.
Sikkim is a state situated in the north eastern part of India, sharing its boundaries with China, Nepal & Bhutan. Hence, being bounded three ways with international borders; free movement of the outsiders (tourists/businessmen) is partially restricted and heavily supervised.
By all means, yes. Sikkim is a heavily conserved biological hotspot that needs constant tending. Mass littering can damage the ecosystem to a large extent. Hence, littering is a seriously punishable offense in Sikkim. And so is spitting & smoking.
The Gurudongmar Lake & the Nathu La Pass are strictly closed off to the foreign nationals due to its close proximity to the international borders.
No. You have to visit the traditional offices for the procedure of issuance but the registered tourist agents you have hired can cover the task for you before the commencement of your vacation.