Hey Pert,
thanks again! Today I was able too look a bit deeper. I thought ist maybe a good Idea to give the Terminal a few minutes to display something. And....what a surprise. I got an error. Which I don't understand right now, but we getting closer.
/Applications/Arduino.app/Contents/MacOS/Arduino
2017-11-25 00:54:46.103 Arduino[1584:35488] kCFURLVolumeIsAutomountedKey missing for file://localhost/Volumes/MC_backup_chris/: Die Datei „MC_backup_chris“ konnte nicht geöffnet werden, da du nicht die Zugriffsrechte hast, um sie anzuzeigen.
Strange, because MC_backup_chris is my TimeMaschine Backupshare on my Server. I do not have permissions to read it as my user Chris, but as root.
So next step of course. sudo /Applications/Arduino.app/Contents/MacOS/Arduino And guess what. It started... at least a solution I could life with, for a while 
Closing and reopen as chris-User didn't work. With a quick search what kCFURLVolumeIsAutomountedKey is exactly, it seams to be some strange Apple stuff. I found some Java Errors, some Xcode errors but didn't went further.
When I went to bed last night, I left the Terminal open, and found the following stuff this morning:
(started with User rights, no root.
/Applications/Arduino.app/Contents/MacOS/Arduino
2017-11-25 01:07:33.784 Arduino[1673:46800] kCFURLVolumeIsAutomountedKey missing for file://localhost/Volumes/MC_backup_chris/: Die Datei „MC_backup_chris“ konnte nicht geöffnet werden, da du nicht die Zugriffsrechte hast, um sie anzuzeigen.
2017-11-25 01:12:09.928 Arduino[1673:46684] IMKInputSession presentFunctionRowItemTextInputViewWithEndpoint:completionHandler: : [self textInputContext]=0x0 *NO* NSRemoteViewController to client, NSError=Error Domain=NSCocoaErrorDomain Code=4099 "The connection from pid 0 was invalidated from this process." UserInfo={NSDebugDescription=The connection from pid 0 was invalidated from this process.}, com.apple.inputmethod.EmojiFunctionRowItem
java.net.SocketException: Can't assign requested address (Error setting socket option)
at java.net.PlainDatagramSocketImpl.socketSetOption0(Native Method)
at java.net.PlainDatagramSocketImpl.socketSetOption(PlainDatagramSocketImpl.java:74)
at java.net.AbstractPlainDatagramSocketImpl.setOption(AbstractPlainDatagramSocketImpl.java:309)
at java.net.MulticastSocket.setNetworkInterface(MulticastSocket.java:554)
at java.net.MulticastSocket.joinGroup(MulticastSocket.java:320)
at javax.jmdns.impl.JmDNSImpl.openMulticastSocket(JmDNSImpl.java:463)
at javax.jmdns.impl.JmDNSImpl.<init>(JmDNSImpl.java:420)
at javax.jmdns.JmDNS.create(JmDNS.java:81)
at cc.arduino.packages.discoverers.NetworkDiscovery.inetAddressAdded(NetworkDiscovery.java:192)
at cc.arduino.packages.discoverers.network.NetworkChecker.run(NetworkChecker.java:62)
at java.util.TimerThread.mainLoop(Timer.java:555)
at java.util.TimerThread.run(Timer.java:505)
Cheers, Chris