I am working on a Typeface at the moment and have done all the letters so far. Now it comes to Spacing and Kerning. .
Am I allowed to use the Metrics of that existing font (not designer by my self)?
You mean the LSB and RSB? It’s likely going to be not the spacing you want, because different designs require different metrics. Better use the Letterspacer scripts. See the Extend page.
The complex of Metrics, spacing, kerning, and sidebearings are all part of intellectual property and can not be used without consent of the original designer.