Importing Illustrator Layers into Premiere Pro

To have access to the Illustrator document Layers and animate them, the current workflow would be to import the layered Illustrator file into an After Effects project as a Composition and then import the resulting Composition into Premiere Pro.

If the Illustrator file is already placed in a Premiere Pro Sequence, right-click and choose Replace with After Effects Composition.  Once in After Effects, right-click on the Illustrator file and choose Create > Convert to Layered Comp or Create > Create Shapes from Vector Layer.  Then animated as needed.  Save in After Effects whenever you are returning to Premiere Pro to make sure what's happening in the linked After Effects Comp is current.

This means having an After Effects project file to keep track of.  I like to save it next to the Premiere Pro project file for smaller projects and sometimes in a folder named something like "Linked After Effects Comps" that's next to the Premiere Pro project file.

As with any Illustrator file imported into After Effects, an object that needs to animate separately must be on its Layer at the root level of the document (that is, not on a Sub-Layer).

You can import Photoshop layers in PP.  Is it possible to covert the AI to PS?

You cannot select a layer in Premiere as it as you already discovered.

If you want to change a layer you can open the file from Pr (edit original).