I don't have a TMGC+C, but I'll answer your questions from everything that I've heard about it. Some of my answers might be wrong, though.
1. As far as I know, you can only cook on the Entama and Uratama.
2. There are seven secret items. After finding one, you will get a happiness symbol underneat your happiness bar. This will increase the length of your Tamagotchi's happiness bar so it takes longer for it to be very unhappy.
3. The door icon lets you go out to different locations. One is the Game Centre, where you can play three games. The others are called Tamatama Market, where you can buy items, Gotchi Reform (well I think that's what it's called anyway), where you can remodel rooms in your house to different styles (for example Japanese style or Royal) for a fee, Gotchi Park, where you can talk to different characters that are also at the park, a Prize Centre, where you can use lottery tickets (don't know how you get them though), the Matchmaker's house, a Theme Park (I'm not sure what you do there except for possibly just going on the rides), Tamagotchi Department Store, which is probably just another shop that sells different stuff to the Tamatama Market, Celebria (which I think is a movie theatre) and the Gotchi King's castle which is unlocked after finding all seven secret items. Here you can play a game to earn more Gotchi Points.
4. The hunger and happiness meters are both on the first screen of the Check Meter. Hunger's shown by rice bowls, instead of hearts. Happiness is shown by a bar which increases as you find the happiness items.
5. Setting the time is the same. As far as I know, normal numbers are pretty much international. Some languages like Japanese and Chinese might have special characters for numbers, but as far as I know normal numbers are used far more often. I see them on the Japanese Tamagotchi site all the time when they give the date for when a certain Tamagotchi will be released. So don't worry.
6. There are three normal games and a secret game. One is a flip card game. You'll be given a moment to look at the cards. Then you must choose two cards to flip over, using the A button to scroll and B button to select. You've got to try and match all of the cards within the given time amount. You must also try not to flip over the Death God cards. Another game is a game where you need to catch the apples, similar to Get the Notes on the v3 but I'm pretty sure on this one it's A to move left and B to move right. The third game is a shooting game, where you use the A button to move the bow down and the B button to fire. You've got to try and pop all three balloons in a short amount of time while trying not to hit the Death God balloon. The secret game's played the same as the apples game but you're catching Gotchi Points instead.
7. Yes. TMGC+C are incompatible with any other version.
