There is absolutely no way to turn off your tamagotchi. You have to hold down button a and b at the same time and it will pause your tamagotchi. To fill your happy hearts, give your tamagotchi snacks or play games.
My friend's old-fashioned v1 did the same thing. It's because one is too advanced for the other to know what kind of tamagotchi characters it has. So it looks like a random black blob.
You need to keep it unpaused. It will grow if you keep it unpaused. That's the best I can tell you. I don't have any cheats for growing faster, but if you go to www.gamewinners.com and go to cheatsm handheld games, tamagotchi v2, you may be able to find a cheat for making it grow bigger
I think you just select v1 on your v2 and, of course, other on your v3. A boy in my class has a v3 and him and someone else tried it, but I don't know if it worked.
Your tamagotchi need to be the same age. That or you need to use the love potion. I found a lot of cool tamagotchi cheats at www.gamewinners.com. You may be able to find something there :marumimitchi: . My tamagotchi's a UFOtchi. It's only one year old, but I went to a v2 character chart...