No, there is no flights to Tawang. Better you reach Guwahati first by flight, then Tezpur by road and after that Tawang. It is worth to mention that u can't reach Tawang from Guwahati in a single day due to road condition.
Since there is no direct train or flight between Guwahati and Tawang, the best way to reach Tawang is by road. The total distance is 500 km and takes about 13 hours via NH229. There are several stop over options available on this route. You can choose from the following options according to you convenience- TEZPUR, TIPI, BHALUKPONG and BOMDILA.
It depends on what it is you want to see. I'd say hit Gangtok first, then Tawang and the Cherrapunjee. Avoid Cherrapunjee in the monsoons because it can get REALLY wet. It'll be spring-summer, so sightseeing in these places should be pretty easy. There isn't great flight or rail connectivity in these parts, so don't forget to factor in the travel time between these places. Also, there'll be loads of tourists during this time because of the summer vacations, so make sure your stay and travel is booked in advance before going.
That really depends on your reason to travel. Whether in a group or solo, Tawang is a beautiful place to visit. However, due to the terrain, it is smarter to backpack because road connectivity isn't all that great. Your budget again depends on how you want to spend your time here, but generally it is pretty inexpensive. Food, stay and travel for 3 - 4 days shouldn't cost more than INR 10,000
As Arunachal Pradesh falls under restricted area, Inner Line Permit is required to enter the State. The ILPs are issued by the Issuing authorities of Government of Arunachal Pradesh with offices at Delhi, Kolkata, Tezpur, Guwahati, Shillong, Dibrugarh, Lakhimpur and Jorhat.