You add game friends in Sims Mobile by
1) Sending a request while at a party. Click on a sim that looks interesting to request. They can accept or ignore.
Or
2) If you know their friend code, you can send a request from the menu that pops out from right side. Go to friends tab (2nd one down) and then to top tab farthest right. You can type in their code to request them as a friend. See picture. Again, they can accept or ignore.
If you want to give out your code so others can invite you, it's on same tab.
In the picture, I backed out my friend code as my friend list is full, so I can't accept new requests. If you don't get an answer back, it might be because they have a full friend list. A problem with the game is they have no way to let you know why they ignored your request.