I have a ATmega32-16PU microcontroller which have 32 KB memory and about 2 KB memory inside EEPROM, but as we know, the EEPROM has a cycle limit.
Can I use the microcontroller Memory, without using the EEPROM ("avoid using EEPROM")?
What pins is the EEPROM and how does the code look like?
Does the microcontroller itself have any cycle limit or lifetime?
The cycle limit is on writes, not reads.
You should be writing non-volatle configuration data to the EEPROM, and volatile data to RAM.
The write limit is usually into the several million writes before the EEPROM becomes worn, so I wouldn't worry about wearing it out during development.
You don't mention what language or development tool you are using, but usually there are specific routines/calls/pragmas for readign and writing to the eeprom, if you aren't specifically calling them, the chances are you are not writing to the EEPROM.
Normally only the bootloader is burnt into the EEPROM, user programs are loaded into RAM, memory writes/reads by the user program are in RAM (unless they specifically try and store some non-volatile data back into EEPROM).