In desktop mode I can go directly into the card and launch any media (photos, music, videos, etc.). The first time you launch the media you will be asked what app you want to use as the default. Indexing is not required.
Regarding copy/paste: yes, you can do so from the card to the desired C drive folder just as you can from a USB thumb drive. However, I leave the SD card in the Surface to save room on the C drive.