Jurgen, great that you have node.js up and running. If you go back to the OpenSprinkler Weather Service github page above then you should see a section titled “Installing a Local Weather Service onto a Raspberry Pi” that leads to some very detailed command line instructions. You should follow Steps 2-5 to get a service up and running. You can then skip forward to Step 7 to test that the service has been installed correctly. However, from memory, Synology does not use “systemd” to make programmes start-up at reboot so you will need to use an alternative solution for Step 7. I believe Synology uses “upstart” but you may need to do some googling to get the sysntax/file location.
If we can get the local Weather Service working on the NAS then we can move on to the network side of things.
Let me know how you get on.