Is it permissible to take a mobile device from the devices displayed at the police station, knowing that a device was stolen from me, and I was told that they would display devices for me to choose from?

It is permissible for you to take your device if you find it displayed and its identifying marks are clear, and it is permissible for the one who displayed it to hand it over to you. However, if you do not find it, it is not permissible for you to take any other displayed devices, because they have an owner, and the property of a Muslim is not lawful except with his willing consent.