compulsory shinkansen reservations

I am going from Tokyo to Nozawa onsen via Nagano next friday and have not been able to get any solid information from anyone about shinkansen reservations.
I would like to know:
1. Is it compulsory to have a reservation for this trip?
2. If not, is there a chance i wont get let on the train or have to stand?
3. How much is the reservation cost generally? If its only a few hundred yen then i would not have a problem paying it.
4. If i buy a ticket from Shinjuku, does that cover all transfers and trains on the trip, as the shinkansen is only from Omiya to Nagano.

Thanks for the help

Is it compulsory to have a reservation for this trip?

No! The shinkansen trains to nagano also have unreserved seats.

If not, is there a chance i wont get let on the train or have to stand?

Only on busy days in the beginning of holidays or during evening business rush hours. But even then, if you stand in line early enough at Tokyo Station, you can secure a seat.

How much is the reservation cost generally?

About 500 yen per person. Free with the Japan Rail Pass or JR East Pass.

If i buy a ticket from Shinjuku, does that cover all transfers and trains on the trip, as the shinkansen is only from Omiya to Nagano.

If you buy at Shinjuku, you will get the following two tickets: One for the base fare from Shinjuku to Nagano (via Omiya) and one for the shinkansen supplement from Omiya to Nagano.