Switching Shinkansens

We are flying into Narita and going straight to Hiroshima for our first leg of the trip. We are wanting to catch the shinkansen for this.

I've worked out we need to take the NEX to Shinagawa Station and then jump onto the Nozomi line to get down to Hiroshima.

My question is - can I purchase all of my tickets at Narita airport or do I need to purchase my ticket to Hiroshima at Shinagawa Station when I get off the Narita Express? thank you !!

Yes, you can buy everything at Narita Airport.
Generally speaking: you can buy any JR regular ticket at any JR ticket office in the entire country.

Yes, you can and you SHOULD buy a "through ticket" at Narita Airport, because it would slightly be cheaper than buying them separately.

(To be precise, you'd be buying a through basic fare ticket from Narita Airport all the way to Hiroshima, and separate express fare tickets for NEX and Shinkansen.)

Cheaper again if you get a unreserved seat. And jump on at Tokyo instead of Shinagawa. As the train starts at Tokyo. And much higher chance at getting a seat.

Agree with answers above

You can also change to Nozomi at Tokyo station instead of Shinagawa. Although Shinagawa is smaller and easier to handle. It probably makes no real difference where you change.

Shinagawa is a bit smaller than Tokyo (not really that much smaller), but one advantage of changing there is that the arrival track for the N'Ex is close to the transfer gate to the shinkansen. At Tokyo, arrival at basement level 5 on one side of the station and walking 5-plus minutes to the other side of the station to catch a shinkansen simply takes longer and walking with luggage through the crowds is less pleasant (directions to the shinkansen tracks are very obvious and simple though).
Note for the OP - you will be getting a Nozomi service (name of the train) on the Tokaido shinkansen line.