DGX station and extra software

Does anyone know if I can install extra software like Java JDK or MongoDB database on a DGX station?

Yes you can.
However for any such software you will be on your own for support/use. The software supported for DGX products is based on the OS/packages that the unit shipped with, as well as the containers that are part of DGX registry/NGC. If you do something to the base environment that makes other software non-functional (e.g. containers) and you ask for help, its likely that you will be asked to restore your DGX (incl. station) to its original configuration.