Recently , I transferred one of my previous wizard's items in buck to my new one with the shared bank. But it feels like some of them are missing. Can friends take things from my shared bank and can I give others items that I have?
No. Only characters on your account have access to the Shared Bank.
The trade of items between different account logins will not be added to Wizard101.
The only items that can be traded between two different account logins are non-enchanted Treasure Cards.
Items that you want to place in the Shared Bank can be moved between Wizards on the same account. If you can't use the item, sell it to the Bazaar, and if it is marked No Auction, you can sell it at the regular shopkeeps throughout the Spiral.
We feel that an economy of item trading is not appropriate for our game. KingsIsle Entertainment has developed Wizard101 to be an exciting and fun online experience for people of all ages. We believe that an important part of delivering online entertainment is to provide a safe environment for all players, and that’s a responsibility we take seriously. Introducing an in-game item trading economy does not fit with our values and vision for Wizard101.
Personally I wish you could trade items between accounts in your family but I can see where in general this would be abused very easily since I see very often children getting scammed out of their treasure cards, they would have a field day with this one.
Altho you can visit someone else's house and use thier bank it is your items you will see not thiers.