Is it permissible to keep pictures of the deceased in the house? And is there anything in the Sunnah of the Prophet that prohibits this?

It is not permissible to request or keep hand-drawn images of the deceased, as they fall under the category of forbidden images, which were prohibited in the Prophet's (peace be upon him) saying: "Do not leave any image without obliterating it." The reason for this prohibition is the imitation of Allah's creation. As for photographs taken by a device, some have permitted them because they are not an imitation of Allah's creation but rather a reproduction of images that Allah has already created. If there is no need for photography, it is better to avoid it to steer clear of doubt. Photography is absolutely forbidden if it involves something that is not permissible to look at, such as private parts or women, unless there is a necessity. It is better for the deceased to be prayed for and to have charity given on their behalf. Keeping their image may lead to their veneration and then their worship, which is why keeping images of the dead is prohibited as a preventative measure.