Yes the Civic head unit is just basically an android tablet. You can add your own wallpapers (non-moving, just photos).
No you cannot install APKs or Apps or anything else. Honda locked it down pretty good. If you browse the "Electronics" forum section you can find many discussions going on about how far people have gotten in hacking into the head unit
Add photos onto a FAT32 formatted USB key and follow the directions of the video at the top of this thread but instead of clicking "live wallpapers" just click "wallpapers" and then I believe the next option was "photo album" and it should find your USB
EDIT: photos cannot be in folders... They must be located in the root directory of the USB key