Question:

Does Salesforce Support Dataloader, Workbench, Salesforce Inspector?

Answer:

Officially, Salesforce (SFDC) Support only supports SFDC Dataloader. Workbench, Salesforce Inspector or any Third Party applications/extensions are not within the scope of SFDC Support. 

Related Documentation:

Salesforce Help Documentation: 

• Installing Data Loader
• Salesforce API and Data Loader versions

Third Party Documentation:

• Workbench Documentation