Yes, when you purchase coins from the Coins and More section, your bank account balance will be increased by the number of coins shown in the item you buy. There are other items in there that permanently lower the cost of food and medicine, and increase the number and value of collectibles that appear in the yard.

Our games don't support syncing between devices. There are different opinions about that, but we have chosen to have one family per device. Many people like having different families when they have multiple devices, and syncing families between devices would require an Internet connection in order to play. We think that's an inconvenience that many people would rather avoid.