During recording the following error appeared: "E501 Insufficient free space on media." Can I have it automatically delete old files when there is no more free space on the CF card?

Yes, turn ON the media FIFO function. If the CF card does not have sufficient free space, or if there are 1000 files or more, old files will be overwritten with new ones.

For details on the media FIFO function, see Explanation of functions: Data Saving Function
in the user's manual.

DX1000/DX1000N user's manual
DX2000 user's manual