The original DekaTama Shop models came in seven different configurations - with each of the seven regions in Japan getting certain region-specific items. These Deka Tamas were for use with the Keitama and Akai-Series (the Tamagotchi with the red screen.)
Later, Bandai released the Tama Tama Market, which contained all the region-specific items together. The Tama Tama Market was for use with the Keitama, Akai-Series, EnTama, and UraTama (the Tamagotchi with the blue screen.)
The above Shop/Market models had yellow-orange colored shells.
There were also a few special Shop/Market models.
The Tama Royal Market had more exotic items. It had a pearl-white shell, with "TAMA ROYAL" written across the top of the screen in English-alphabet letters. I believe it worked only with the EnTama & UraTama.
There was a shiny gold plated "Gotchi King" Deka Tama. I'm not sure what the "present" you would receive from it was. (It might have been a money tree.)
In addition to the Shop/Market models, there was also a Game Center DekaTama. It can be used with the Keitama, Akai-Series, EnTama, and UraTama. As far as I know, there was only one configuration; no region specific Game Center DekaTamas. The Game Center DekaTama had a red shell.
The three or four letter / number combination printed on a small white sticker on the back of the Deka Tama identifies which model it is. Here is a partial list:
D03 = DekaTama Shop - Edokotchi (for KeiTama)
D04 = DekaTama Shop - Shachitchi (Chubu region)
D08 = GameCenter
EB03 = Tama Tama Market
You'll have to check the rating on their AC adapter to determine whether you'll need a convertor. I believe the AC adapters that came with the Tama Tama Market are marked 100 V, 50/60 Hz. Power in the USA is normally 115-120 V, 60 Hz.
I've never seen a Deka Tama with missing pixels, but I suppose if the contacts go bad, a row or column of pixels could become faded or missing.
p.s. Prior to the Deka Tamas for the Keitama, there were some released for the Tamagotchi Plus (the model Tamagotchi that came out before the Keitama.) These had a white shell.