Yup. Classic Dove MacSnap (most likely). Requires 800K disk upgrade and 128K ROMs.
Nope. One easy way. Look at the serial number under the front left bezel. If it was made before October 1985, and ends with "...M0001" (not M0001W, D or E), then it most likely started life as a 128K.
And once again, the case back was not replaced, just the label/badge.
Also, I don't recall, did the 512K upgrade kit also come with a replacement agency label? If your agency label says Model M0001 (not M0001W, D or E), then that's a sure sign it was a 128K first.