Sorry for the late reply!
Tamatown is a website on the internet that's connected to Tamagotchis. There is a different Tamatown for every version of tamagotchi. On some Tamagotchi's like the V3 and V4, you choose a username for your tamagotchi(on the actual device, not the computer), but then you enter the username into Tamatown and you get codes to enter in to your tamagotchi for different items. It may seem a little confusing at first, but everything is really simple! The new Tamagotchi Music Star(V6), and Tama-go(V7), can access a different Tamatown site called Music City. Of course Tamatown is optional, as I don't go on Music City, but I think you can get different items from there to your tamagotchi. There are also another thing called shop passwords, when you go to the shop on your tamagotchi, and from looking up the passwords online, you can unlock secret items too. Each button is assigned a letter, A, B, or C, so when you get the passwords online for the shop, it might say something like A B A C B A C, which means you press the first button, second, first, etc. The codes for Tamatown and the passwords for the shop are in fact two different things, just so you don't get confused. Also, no, Tamatown is not disconnected from the U.S.
Sorry, a P1 and P2 are the two original Tamagotchis that came out in 1997. They have very limited features, no connection, but since they're so rare these days, worth quite a bit of money if you want it new in box. I myself don't have one but I hope to buy one soon, I just have to find one thats cheap!
And for the connections, I'm not very good with know which versions connect with which. I'm pretty sure you can connect the V2's, V3's, and V4's altogether(example v2 and a v4, v3 and a v2, etc.), but I'm not quite sure about the others like the V5, V6, Tama-go(newest version), or V1. Don't take my word for it, but I'm pretty sure the V5's can only connect with a V5 because it has a "family" feature including three tamagotchis instead of just one.