1. to visit any foreign country, a passport is required. visa won't be required for Indians in Bhutan 2. December will be cold. the right time will be maybe in march or April 3. it depends on how many people, mode of transport, adaptability leve, etc. but if you are okay with budget travelling, it shall not cost more than 45000 per person. it will cost way lesser though
Passport isn't required, carry your identity cards to get a pass issued. it requires half a day to get that done. temperatures will be low.
depending on the level of luxury you desire, it will cost you starting from 10k per person