Go to bank and click "Transfer money" for nuffies. For icons, do the normal procedure to buy them and you'll find an option called "Users" under myself. Select it and type the username of the person you want to gift it to.
Giving money; you need to go the person status profile, and click the money they had under their name.
When you go to shop home. Press an icon, there's an option to gift it to someone else. You have to type their name and make sure to click on the option "users".