Neopets is a very popular game where you raise a pet, you can find it at Neopets.com. There are a few other games, but most of them don't offer as much flexibility. You can check Kongregate.com for some related flash games, but if I were you I'd stick to Neopets.
Yes, but most of them are Internet games
Some good websites to find pet grooming games would be: http://pet-grooming-games.cooking-games.biz/ or http://pet-grooming-game.dressup.me/.
Well here are some games: Neopets PetPetPark Wizard101
clubpenguin.com
Not all games. But some games you must have the internet. When you go to buy a game it will tell you whether or not the internet is needed.
It is a form of opinion whether or not Internet games are fun. For most people, Internet games are enjoyable and fun. However, some think that Internet games aren't fun, but are a waste of time.
playing games
Petville
You can obtain and play pony games online at sites such as Pony Island and Pet Games. You can also download a My Little Pony game to your phone or tablet.
to download games you need to have the apple site which is on the internet. To play some games you nedd wireless internet wherever the itouch is but this is not true for all games yet it is helpful.
Go To Shockwave.com
On the internet.