Is it permissible or impermissible to collect and publish medical books, some of which are free and some of which are paid but were obtained for free from the internet, on a single website for general benefit, with a small profit that covers maintenance costs?

It is not permissible to download non-free books without the permission of their owners. It is necessary to limit uploads to free books and delete all others. The rights of the owners of non-free books that have been infringed upon must be acknowledged and compensated for, either by delivering the compensation to them or by seeking their forgiveness. If that is not possible, the value of the compensation should be dispensed with by spending it on charitable causes. There is no harm in benefiting from the website's profits.