If I make a maven repository available for others to use, do I have to get permission form the authors of those software that I host in my repository even if they are free software?
Can I host free software libraries under any license or should they have compatible licenses?
Free software can be redistributed without restrictions (other than providing the source code, which is required in some licenses, but I assume that is actually what you would be redistributing).
The license of the libraries you host does not need to be the same or compatible, for redistribution purposes. If you do not change the source code in any of those libraries (e.g. mixing them up), you should be fine.