How do I update or add new symbols from the online database to the DSE library ?

Extract/import symbols using the unarchive function. You can use this for models imported from the online catalogue: https://designspark.zendesk.com/hc/en-us/articles/211373889-How-can-I-download-additional-parts-and-libraries- 

Alternatively, use Import DWG to place AutoCAD DWG symbols into library.

Make sure to select the correct class for your symbol. You can associate a symbol with a specific manufacturer part through the symbol properties.