It goes in order like up to the Kuribotchi, the rest is teens and then up to the oniontchi, it means the rest are adults. If they're blue on the tamadex, it means they're a even generation of tamagotchi and if they're purple on the tamadex, they're an odd generation of tamagotchi.
Ya they have to mate to have the next generation of your tamagotchi and you have to mate with another tamagotchi that has a boy by connecting or you can wait for the matchmaker to come.
a matchmaker is a person that arranges marriages for tamas that don't have a partner. if you have a friend that has a tamagotchi, you can connect and the friendship level will increase when you connect a few times and you can get a partner by connecting.