Tokyo train questions

Shinjuku Prince hotel is my base of operations.

1. Is the quickest way from Shinjuku to Tokyo Station the JR Chuo line? Or one of the subways? I'll have the Suica & N'EX Combo, can that be used on the subway?

2. Shinjuku Station will be crowded, I get that. Is it crowded as in waiting in long lines creeping toward the trains? Or is it just a rush where you can move if you flow with the crowd?

3. It will be me and my wife, plus a 5 and 1-year-old. My plan is to just carry each kid and sling the stroller like a backpack. Not perfect, but it sounds better than pushing a stroller or holding hands and walking.

4. What are the rush hour times?

5. My daughter is 5 years old, so that means she's under the child age of 6 (per the NEX site: "infants (1 to 5) generally travel free"). Does this free travel for 5-year-olds also apply to JR-East trains and subways? I'll assume they'll want to see a passport to prove she's under 5. Does this mean I'll have to always go to a manned ticket booth at each station?

Is the quickest way from Shinjuku to Tokyo Station the JR Chuo line?

Yes.

I'll have the Suica & N'EX Combo, can that be used on the subway?

Suica cards can be used on virtually all trains in Tokyo, including subways. On your ride to/from the airport, however, you have to use JR.

Shinjuku Station will be crowded, I get that. Is it crowded as in waiting in long lines creeping toward the trains?

Only at some bottle necks, there will be actual traffic jams of humans. But generally the stream of humans is moving at a medium to fast speed.

4. What are the rush hour times?

Shinjuku Station is particularly busy between 7:30 and 9:00 on weekdays. And very especially so between around 8:00 and 8:45.

Does this free travel for 5-year-olds also apply to JR-East trains and subways?

Yes with some exceptions regarding reserved seating, as explained on the following page:
http://www.japan-guide.com/e/e2359_001.html

5 You can take your daughter�fs hand and pass through automatic ticket gates. I did so when my kids were younger.

"4. What are the rush hour times?

Shinjuku Station is particularly busy between 7:30 and 9:00 on weekdays. And very especially so between around 8:00 and 8:45."

So, hop on before 7, I should be okay (relatively speaking of course).