So, I am not seeing an option to add a friend on my nook phone, and we just had an online session. And I customized an item, but for some reason I can't drop it like other items
the add friend has to come from outside of the game. go to the home screen and go to your profile. once there on the left youll see a section where you can add your friend
also, none of the customized items can be given or sent to anyone...is that what you mean? or you just cant remove it from your inventory?
What you need is the "Best Friends App" to get that you must talk to Orville, ask him that you want to fly, and then select "Search for a Friend" and then he will give it to you. Then you must open the app on your phone and check to see if your friend is there. If they are send them a "Best Friend Request" and make sure you tell them to accept it. Once you done that, you can now send gifts to your friend.
Hopefully you figured it out ok, but just to clarify, you can't gift items with custom designs (yellow leaf), and you also can't drop those items on the ground. You can only place them or put them in storage.