can the data inspector only visualize one layer at a time?

Sure, you can have many layers. If you open the Data Inspector as a stand-alone application, use the Add dataset button:

If you start the Data Inspector from your workspace, eiter use an Inspector transformer for each layer, or define a Group By in the Inspector, which will force each group as a separate layer.

Yes you can, but it's a bit tricky. The "Open Dataset" option opens the data in a new view, you need the "Add Dataset" to import another dataset into an existing view.

In Workbench you can place multiple Inspector transformers, each one will become a new layer in the Data Inspector.

Hope this helps.

Or if you want to visualise each layer individualy you can use one inspector with the group by setting.

This will split and visualise the data according to the values found in the attribute used in the group by setting.