Is it permissible to establish an electronic library that includes a section for learning and maintaining computers, while fearing its use in the trade of devices that may contain illicit materials (movies and songs)? And should this section be removed or kept?

The default rule for sciences like these is permissibility. Therefore, there is no harm in disseminating them with the intention of benefiting people. The fact that they might be used for unlawful purposes does not change the ruling of permissibility to prohibition. However, if it is highly probable that most users will employ them to commit sins, then removing them for this reason is good.