Flying into Nagoya

My friends and I are flying into NGO, staying there for one night, and then moving on to Nagano from there. We would like to seek the advice of either people who have traveled to Nagoya or who have lived in Nagoya:

1) Our flight lands in Centrair at 8pm on a weekday, and we are taking the earliest train the next morning to Nagano. Will the Rail Pass office at the airport be open still after we go through immigration? We need the rail pass for the next day, and we're leaving Nagoya station on the 7am train, so would the Rail Pass office there be open early enough for us to exchange our rail passes?

2) Since we're arriving at 8pm, I assume we won't be on our way to our hotel until after 9pm. Would it be a better idea to stay at a hotel near the airport or near Nagoya Station (we're leaving on the 7am train the next morning)? We're budget travelers, so are there hotels within 5 minutes of either the airport or Nagoya Station that are about or under 3,500yen per person? We're all girls, so capsule hotels might not work if they're men-only.

3) Are restaurants serving local specialties open at 10pm or later? I want to try some Nagoya dishes and dinner is the only meal we'll have in Nagoya. What's famous in Nagoya? I heard noodles are, but what type of noodles? Are there any specific restaurants (that can easily be accessed either from the airport or the station) that you would recommend?

Thanks in advance to anyone who can help.

Will the Rail Pass office at the airport be open still after we go through immigration?

There is no rail pass office at Nagoya's airport. The closest one is located at Nagoya Station. The train between the airport and Nagoya Station is operated by Meitetsu Railways:
http://www.japan-guide.com/e/e2431.html

We need the rail pass for the next day, and we're leaving Nagoya station on the 7am train, so would the Rail Pass office there be open early enough for us to exchange our rail passes?

The ticket counter at Nagoya Station will be open before 7am. You just have to find the correct one.

Since we're arriving at 8pm, I assume we won't be on our way to our hotel until after 9pm. Would it be a better idea to stay at a hotel near the airport or near Nagoya Station (we're leaving on the 7am train the next morning)?

I personally would prefer to start the day at Nagoya Station.

We're budget travelers, so are there hotels within 5 minutes of either the airport or Nagoya Station that are about or under 3,500yen per person?

I don't think this exists at the airport. Possibly you can find some cheap accommodation around Nagoya Station. A business hotel, for instance.