It maybe required to access your router in order to setup a VPN or to be able to gain remote access to your systems data, changing your router later will likely cause these connections to fail.
The database server can be on one of your workstations, or on a dedicated server.
The only requirement is that the server will need to remain on at all times, and because of this, you may wish to use a dedicated server.
Mobile app server
If you choose to use the mobile app solution, it will need an additional software server, this may well work on a stand alone database server, but it depends upon your requirements, or numbers of devices used.