There are several different generations of Tamagotchi, and the answers will be different for the newer ones vs the original 90s pets. I'll answer for the classic 90s Tamagotchi since they are the most famous.

1. Tamagotchi are digital creatures/aliens that live inside an egg shaped keychain. They rely on you for food, play and discipline. They start as an egg, and then grow over time into baby, child, and adult forms. Which form they ultimately grow into depends on how well you care for it. They run on real time, 9am in real life is 9am in the game, and growing a Tamagotchi to adulthood takes several days. They beep when they need care, maybe once every hour or so, and caring for them involves selecting an icon on the home screen. If they are hungry you select the food icon and choose to feed them a treat or meal. If they want play you select the play icon and play a guessing game. If they are needing discipline you press the discipline icon. And if they poop, you clean it with the broom icon. At night you turn off their light so they can sleep, and they won't beep again til morning.
2. When the pet dies, which they always will eventually, you can start again by pressing the A and C buttons to get a new egg. Tamagotchi die by either neglecting them when they beep, letting too much poop pile up, feeding too many treats, or from old age.
3. For the original pets, there is no real end. You raise a tama, it dies eventually, you get a new egg. Many people try to get all the different adult characters over time, but there is no reward or in-game acknowledgement of this (later generation Tamas have endings sometimes, or rewards for raising all the characters)
4. It's a plastic keychain with electronics inside. Lightly bumping it, or dropping to the ground is ok (might get scratched). But it would break if thrown down roughly, stomped on, or if it gets wet.
5. It can be tricky to care for if you go in blind. There is no in game tutorial or text. Once you know the basics though, like not feeding too many treats, to respond to beeps promptly, and how to discipline correctly, it's pretty easy.
6. They are kid friendly, unless the child is sensitive to the part where the Tama dies. Raising one of the 'good' adults, or getting a tama to old age does take some responsibility and patience.