Advice needed on JR trains

Good morning,
We will be arriving at Narita Airport at 7pm on a Saturday night, what time is the last NEX train to Shinjuku???
Does the NEX train go all the way to Shinjuku or do we have to change trains ?
I have used Hyperdia but cant seem to get the NEX train up, only the Keisei trains timetable comes up. I presume we will take at least 1hr to 11/2hrs to go thru customs, immigration and to the JR office to collect/exchange our JR RAIL PASS voucher. I would prefer to get the train all the way to Shinjuku. We are staying at the Best Western Astina Shinjuku.
We will be using our JR PASS for travel for 7 days from Tokyo to Kyoto, To Hiroshima, To Nagoya and back to Yokohama my next question is, using Hyperdia I have selected all the trains we will be catching and making seat reservations on. ( I intend to make my seat reservations at least the day before or days before in each place we are leaving from.) My main question is what happens if we miss the train we have reserved seats on? Can we still use our JR pass to catch a later train on the same day?? Is there a penalty for missing a train you have reserved seats on? ( god I hope this question is not stupid)
As always thank you everyone who takes the time to answer my posts and I greatly appreciated it.
Kindest regards Dee

make sure you only tick the JR lines and untick the Private lines. You will find the N'Ex results then.

Thank you so mu. Dee

As far as not making the train you have reserved seats for, it is customary to take the very next train in the unreserved seats. You can also make another reservation at the ticket window, but I would take the "personal penalty" of taking the very next train unreserved.

When will you travel?
How many travelers will you be?
Have you confirmed that you cannot choose Haneda Airport [HND]?

what happens if we miss the train we have reserved seats on?

If you travel with Japan Rail Pass, you can reserve your seats on a later train, but of course it is highly demanded that you never miss a train if you make seat reservation.
(The seats reserved by you cannot be available to other passengers even if you miss the train.)

Does the NEX train go all the way to Shinjuku or do we have to change trains?

You are highly likely to take a JR "Narita Express" train to Shinjuku. But, your hotel is a little away from the N�fEX platform of Shinjuku Station. You may hope to take a taxi from near New South Gate. (The taxi fare is estimated at less than 1000 yen per car.)
- Shinjuku Station of JR
http://www.jreast.co.jp/e/stations/e866.html
: Here "Narita Express" trains from the airport use Track 6.

Your "Narita Express" train ride to Shinjuku will last for about 1 hour 15 minutes to 1 hour 35 minutes.
"Narita Express" trains shown below are two-destination trains until reaching Tokyo Station, where each of them is divided into two parts.
Shinjuku Station is beyond Tokyo Station, and a "Narita Express" train part bound for Takao or Ikebukuro makes a stop at Shinjuku Station.
All seats of a "Narita Express" require reservation.

Narita Express 50 bound for Takao (and Ofuna)
: Narita Airport (19:46), Airport Terminal 2 (19:49).
Narita Express 52 bound for (Ofuna and) Takao
: Narita Airport (20:44), Airport Terminal 2 (20:47).
Narita Express 54 bound for (Ofuna and) Ikebukuro
: Narita Airport (21:44), Airport Terminal 2 (21:46).

We will be arriving at Narita Airport at 7pm on a Saturday night

Probably JR EAST Travel Service Center in your NRT terminal will get closed before you will become free to travel. You can visit a JR Ticket Office (located just beside the JR gate) instead, where you can turn in your Exchange Orders for Japan Rail Passes and try reserving your seats on "Narita Express" and Shinkansen trains.

We are staying at the Best Western Astina Shinjuku.

You had better make sure not to get lost after the sunset in the area.
The hotel itself is located in a rather quiet district, where also the main office of Shinjuku city ward is located, but Kabukicho area is better known for its red-light district.
http://www.japan-guide.com/e/e3011.html#kabukicho

Tokyo to Kyoto, To Hiroshima

According to the current timetable
: There are three regular Shinkansen "Hikari" trains to depart from Kyoto in early morning (before 8:30) for Hiroshima.
: If you travel with Japan Rail Pass and cannot catch one of these three "Hikari" trains, you will need to change Shinkansen trains on the way to Hiroshima unless an extra direct train is available.

(By the way, will you travel as far as to Miyajima Island?)

and back to Yokohama

Which area in Yokohama will you travel to?
Please note that Shinkansen trains run not via Yokohama Station. The only Shinkansen station in City of Yokohama is Shin-Yokohama Station.

There are no unreserved seats on the Narita Express, however.