Usually, any I2C device peripheral, such as an EEPROM, has an I2C device address.
Does I2C EEPROM have a register type of memory arrangement? I tried to search but was not able to find it.
When the master, Microcontroller, needs to send data or receive data from the device, whether we send or receive data to the EEPROM registers or how is it arranged?
I recommend to read the datasheet. There´s everything you need to know.
Datasheets are often somehow complicated to understand. Sooner or later you need to be familiar with them.
But if you need some "not that technical" informations: Go to youtube and do a search for "I2C EEPROM tutorial".
Also there are a lot of forum discussions here, in the internet, examples with code, with scope pictures.
It´s all available. Just use it.