Animations?

Do the P1/P2 have animations, like the Connections? Like when you randomly see your tamagotchi take baths or drink something on the screen. Or they just move right and left?

No, the P1-2 do not have those kind of idle animations nor seasonal animations. The primary animation they have is moving around on the main screen which for some is moving right to left, while for others it is staying in place and moving their limbs. The P1-2 have other animations as well such as for eating, happiness, anger, sickness, playing the game, and sleeping. Some animations are reused in other contexts, but not in a way that seems out of place. All animations are unique between characters and it can be quite pleasing to see the difference - such as how Zatchi (P2) has such wriggling arms while Zuccitchi (P2) often throws back its head and shows all its teeth.

^ That's true, though some other vintages do have more involved animations (which I'm sure you know about, since you have a lot of vintages!)

Morino has a screensaver where if you don't look at it for long enough there are trees and falling leaves, as well as sometimes you can see a foot stomping on your character which you have to save it from. Angelgotchi has good and bad deeds as well as a bat stealing the cake, Devil has some as well, and Mothra can be seen attacking the tokyo tower.

I guess I do have allot of vintages and will eventually have approximately half of all of them, once I get a P1 and an OsuMesu pair :^) I guess the simplest way to explain the programming and animations of the various vintages is that the P1-2, Osutchi and Mesutchi, and Yasashii are basic versions while everything else is themed. Although the OsuMesu has the mating function which is unique for vintages, it really doesn't make it more than a feature.