The Sims 2: Open for Business - Family Business?

Yes. I had one of my family's build a restaurant and run it. You can even run a business from home.

This is from the ReadMe file for the game (C:\Program Files\EA Games\The Sims 2 Open For Business\Support\en-us)

There are some core objects your Sims must purchase in order to start a business. Most businesses must have either a cash register or a Electrono Ticket Machine. The Electrono Ticket Machine charges customers for the time they spend on your lot using your amenities and socializing. To build a Salon, your Sim only needs to purchase the Ug-No-More Makeover Station. To build a restaurant, your Sim must purchase a podium, industrial stove, and enough table seating for customers. You should also purchase an Open/Closed sign, because without it the business will never close and your Sim and their employees will quickly become overworked and overwhelmed.

yes you can,

you need to get the sim you want to own the deed to the business to call on the phone "home business" and there you have it.

you can run , cafe, resturant, clothes store (if your running H&M Sims), bakery, pet shop (need to have sims 2 pets)

flower shop, toy shop

Yes you can, before one dies you have to let that sim give the deed to the family buisness and it just goes on until they all die lol