The following information was translated from the Bandai Tamaplus Raising Guide (the title in Japanese is "Kaettekita Tamagotchi Plus Suku Suku Sodatekata Guide") and the Bandai 'Playing Book' (Kaettekita! Tamagotchi to Asobu Hon).
Tamaplus Hidden Parameters
In addition to the hunger, happiness and discipline meters, there are three hidden parameters that affect your tamagotchi. These are Luck Level, Body Needs and Heart (literally translated, but should be more broadly thought of as spirit) Needs. Luck Level has an effect on the babies that are born. The other two parameters can have huge effects on the development of your tamagotchi.
Your tamagotchi's luck can range from Level 1 to Level 5. A character with a higher luck level will be offered partners with higher discipline levels for arranged marriages.
A tamagotchi's Luck Level is determined at birth and will not change during the course of its lifetime. However, by marrying a partner with a higher Luck Level, you can increase the Luck Level of the offspring. All partners introduced by Mrs. Busybody have a Luck Level of 1 so babies from arranged marriages will always have a low Luck Level.
The key factors of Body Needs are food, health and discipline. If your tamagotchi's food meter empties, be sure to feed it within 15 minutes of its call. If it becomes sick, give it medicine within 15 minutes of its call. If it calls you for no reason, discipline within 15 minutes of its call.
Clearing at least 20 hurdles in the hurdle game will also have a positive effect on your tamagotchi's Body Needs.
The key factors of Heart Needs are happiness, sleep and comforting. If your tamagotchi's happiness meter empties, give it a snack or play a game with it, but be sure to raise its happiness within 15 minutes of its call. When your tamagotchi falls asleep, turn the lights out within an hour of its call (if you turn out the lights while its yawning, you can fill one happiness heart). If your tamagotchi is feeling insecure, comfort (pet) it within 15 minutes of its call.
Clearing at least 20 moves in the dance game will also have a positive effect on your tama.
Looking at the characters of tamaplus, you may notice that some characters have a counterpart character - Mimitchi and Mametchi, Maskutchi and Gozarutchi, etc. These pairings are related to the fact that certain characters will only appear in certain generations - so Mimitchi and Mametchi will never appear in the same generation.
Characters in Group A and Group C will never appear in the same generation, while characters in Group B can appear in any generation.
Considering that Ichigotchi is the default character for the first generation, it would seem that Group A appears in odd numbered generations, and Group C appears in even numbered generations - this is purely theoretical, however - I could be completely wrong.