Is using a book or a keyboard with symbols of false religions on it (such as the plus sign or the cross), or a flag of a country that contains them, considered an imitation of disbelievers, even if the use is not because of these symbols but for the beneficial content, and is it permissible to watch a beneficial video while muting the sound if it contains music?

Not everything that resembles a cross is a cross; this must be verified. Possessing anything that contains a cross, whether an image or a sculpture, is impermissible before obliterating or dismantling it, because the Prophet, peace and blessings be be upon him, "would not see anything with a cross in his house except that he would dismantle it." It is not permissible to possess it before dismantling, even if there is a need, except for someone who finds dismantling difficult and is in dire need, in which case they may follow those who deem it disliked. Mere possession is not considered imitation unless the possessor intends it as such. As for watching a video with the music muted and the image covered, there is no harm in it, provided there is no other forbidden aspect, because the prohibition of music relates to hearing it. One must be wary of obsessive thoughts.