Andy: "Can I erase an EEPROM by a universal programmer such as SuperProIII?"
The way to answer such questions is always: Read the manual!

This answer is possibly right for the day you receive your programmer. However most (all decent) programmer manufacturers update the software (and not the manual) on almost a weekly basis, so the answer I would give is "pull the devicelist onto the screen".

Bert: "The flash that runs code cannot be erased nor written! You could use a second flash or execute from RAM ! The second option is less expensive but you need ram to do the job".

Let me add that today there are several '51 derivatives with built in ROM bootloaders (e.g. P89C51Rx2) and these can be updated easily.

Have fun,

Erik