Oh, cute! A Donguritchi (the character on your black one) and a Teru Terukotchi (the character on your pink one)!
I'm going to look at the manual in the reference section now and try to answer your questions. I'm really bad at Japanese (I know next to nothing) so please bear with me.
Can you pause them? I don't think so. Maybe you can pause them by going onto the clock setting screen.
How long to they sleep? Probably around the times a normal Tamagotchi does: about 10-14 hours.
What times do they sleep? They probably sleep at the times a normal Tamagotchi does... going to sleep at 8-10pm and waking up at around 8am.
Can they die? By the looks of things they do die, but I have no idea how. Perhaps if you do not communicate them enough?
Is there anything more to do with them than connecting? Well, this isn't really something to do, but they have little animations throught the day. It looks like they wake up or something at 8am, play video games at 10am, have a snack at 3pm and more. And by the looks of things whenever a pac-man like symbol is displayed you need to press the C button to say good morning (I might be wrong here).
Do they grow older? Yes, they grow older. Their growth path is Adolescent -> Adult -> Oldie as far as I know.
Oh and by the way here is a list of characters.
Boy Tamago-chu
ADOLESCENTS
Yangu Mametchi (Young Mametchi)
Yangu Robotchi (Young Robotchi)
Donguritchi- looks like an acorn
ADULTS
Mametchi
Moja Mojatchi- has a lot of hair around his face
Kuchipatchi
OLDIES
Ojitchi
Girl Tamago-chu
ADOLESCENTS
Ringotchi
Ichigotchi
Teru Terukotchi- looks kind of like a sun wearing a dress (can't think of any other way to describe her)
ADULTS
Memetchi
Rabu Zukintchi (Love Zukintchi)- this character is also on the Famitama/v5, she wears a cloth around her head.
Furawatchi (Korotchi/Leaftchi/Violetchi)
OLDIES
Otokitchi
When two Tamago-chu characters mate they live with their babies. The baby characters are here:
Kuchiotchi- this character was also featured on the Entama, looks like a black Kuchitamatchi and is male.
Kuchikotchi- this character was also featured on the Entama, looks like a Kuchitamatchi but with a dark patch on her head and is female.
Rabutchi (Lovetchi)- looks like a heart, this is another female baby.
And two more things, with setting the clock it says nothing about pressing the A button. Maybe you have to go to the clock screen and hold the C button instead. It looks like that to turn the sound on and off you need to go to the clock screen and hold the A button.
The low battery symbol is the same as on the Tamagotchi Connexion versions 1-4. There is still a Load/Reset screen. Load is the top option (yes, it says Load, not the ridiculously odd Download on the Tamagotchi Connexion) and Reset is the bottom option.
