I want that my router will see me as an inside the LAN host when I access him from an outside IP that is not in the LAN so I can access my printer and storage device that are connected to him. I can access his settings but not the storage.
You need to set up port forwarding so your router knows what you are trying to get to. i.e access your router WAN address with a specific port and it will translate that to an address inside your LAN. This way you can map a drive to your storage device and connect to your printer over TCP/IP.
Giving the model of the router will allow more detailed versions of this answer.
ALso I would recommend you look at this answer on SU: What is port forwarding and what is it used for?