Hello, lifou! Hopefully I can answer some of your questions (I live in Tokyo, so hopefully this info will apply to Narita too).
1) Japanese Tamagotchi are exclusively in Japanese, but they're generally quite straightforward to figure out, even if you don't speak the language. I'll go into the particular versions commonly available here in my next response, but if any of these children have played with Tamagotchi before, they should be fine. The colour versions have become slightly more complicated now, but there are many resources here on Tama-Zone.
2) The easiest versions to find here for sale are the Tamagotchi M!x, the Tamagotchi M!x 20th Anniversary edition, the Tamagotchi M!x Sanrio edition and the Chibi Tamagotchi.
The first three are colour versions, and they are the most recent technology-wise. They can communicate with each other and have the most things to do. However, they do have a lot of Japanese. Like I mentioned before, they are quite simple to figure out, but it might be a little confusing at first, especially for the youngest child.
These versions are also fairly expensive. The original Tamagotchi M!x is the cheapest, averaging around 4500 yen. I've seen the Sanrio one sell for as much as 7000 yen in some stores. So buying four of them would be quite pricey.
The Chibi Tamagotchi is more similar to the original Tamagotchi from 1996, only smaller and even more basic. It has very limited functionality and cannot interact with other Tamagotchi. However, it is very cheap (averaging 1500 yen) and is more resilient for tiny hands. It requires virtually no Japanese knowledge and is very low-maintenance, but might become boring quickly.
It might also be possible to find something like the Tamagotchi 4U (another colour version) in Don Quijote (ドン・キホーテ - a discount chain store whose mascot is a penguin), but this isn't too likely.
The other versions will be harder to find and even more expensive. If you happen to travel to Tokyo, you can check out Mandarake in Akihabara/Nakano/Shibuya and they will likely have older versions there; however, they will probably be very expensive.
3) I don't know much about Narita Airport as I've only ever been to Haneda, and I can't advise too much on Omotesando. However, AEON will probably have them (I checked my local one near work today and they were selling the Tamagotchi M!x and the Chibi Tamagotchi). If you can find a Yodobashi Camera, BIC Camera or Yamada Denki, they should sell them too. And, again, certain Don Quijote stores will sell various versions.
AEON has fairly standard pricing. Yodobashi has the cheapest Tamagotchi M!x (that I know of) but the most expensive Tamagotchi M!x Sanrio edition, and it's expensive for the Tamagotchi M!x 20th Anniversary edition too. BIC and Yamada Denki are a bit hit and miss, and Don Quijote tends to sell the cheapest Tamagotchi M!X 20th Anniversary edition if it has it in stock.
I would personally recommend the Chibi for the two youngest children, and regular Tamagotchi M!x editions for the two eldest children. Certainly, the Chibi cannot connect, but it's less likely to get smashed up than the M!x, and will be much easier to understand.
I hope I was able to help! Let me know if you have any more questions - I'm not super-active on this website, so if you want to get a quick hold of me, you can contact me via Twitter (@Chaowzee). Enjoy your time in Japan!