Are Gerber files of inner layers interchangeable?

The Gerber files do not specify the order of layers. As long as you don't use blind or buried vias, the layers can be stacked in any order.

The file names for the individual Gerber files may vary between different CAD systems, and may or may not imply the desired stack-up order.

I always included a "readme" file with my PCB order specifying the desired stack-up order.

If you want to swap the layers directly in KiCAD, the option you need is Edit -> Swap layers.

After swapping the layer contents, you can update the layer names in Design rules -> Layer setup.

To make sure that you didn't make mistake, install an external Gerber file viewer (not connected to or produced by KiCAD). Then, after renaming, view the project in this viewer and imagine what others would see. Assuming you corrected the vias accordingly, yes, you can rename the files the way you want in order to change the layer.