Well... I learned from Tamatalk and the Tamenagerie that you can perform a little trick on your Tamagotchi Connection. This enables you to choose any character you like and have it run in hyperspeed if you want to. The "magic" trick only works for the American Connection or Japanese Plus tamagotchi, so don't bother to open up a Tamagotchi Connexion.
The next "tutorial" will show you what to do. Please don't do this if you want to keep your (shop) guarantee or are afraid to screw anything up. It worked fine for me, but I can't guarantee you that this is without any risk.
Turn your Tamagotchi around so that your facing the back and unscrew it. Ah, that's not so difficult right?
Use a tiny screwdriver (like the one in the picture) to unscrew the four smaller screws. Take the battery out and open your tamagotchi.
Put the battery in again and use a piece of tape to keep it in place. On the left bottom of the battery you will notice a word that says debug, keep your eye on that one.
Now take a regular pencil and rub over those two little silver semi-circles (under the word debug) a couple of times. I scratched them gently for about 8 times. The Japanese plus Tamagotchi uses two squares above the word debugging, rub those.
I guess this makes a lead between the two pieces. I also tried connecting them with a paperclip or aluminium foil, but this didn't work for me.
Don't worry if your egg just hatched like it normally would and you get to choose a name. Just scratch the debugging pieces a little more, don't scratch them off though! Just rubbing would do fine. It took me a while before I could debug my Tamagotchi plus, but the Connection debugged after one try.
So, what to do now? Just choose the character you like best and hit the B button to confirm this. After that you can just raise it like you would with a normal Tama. But you can also use the C button (that's the right button) to speed things up ^_^. This hypertime will automatically stop when your Tama has got to use the toilet or when he gets hungry and so on. After such an event you can press the C button again, untill you get dizzy from your hyper tama character.
They all eat different food, some of them drink something that looks like sake! It looks like not all animations are included. For instance you won't see them falling if you miss a hurdle in the hurdle game. Some of them aren't even showing any emotion at all (O_o). But a lot of them are really nice to explore, it gives you Tamagotchi Connection a whole new dimension ^_^.
The Tamagotchi Connection has got more secret characters than the Plus version. I guess this has got to do with the Keitai Tamagotchi. The Keitai uses some of the characters that are hidden in the Connection, but not in the Plus.