Problem for reading and writting I2C Eeprom 24c02 6

Well, thanks for your answers but I'm at the very beginning with this I2C EEPROM and you get me a little bet lost.

PaulS;
I'm just using a Sketch found somewhere on the web.
As it is my very first go with I2C EEPROM, I'm not really understanding the code actually.
And I'm not a programmer, so till now I've been mostly copying different pieces of code and modifying some part, then look what was happening.

Nick Gammon ;
The WP pin is to GND, so writing should be allowed.

You are talking about 2 Bytes of address that should be replaced by a only 1Byte address because the 24C02 has only 256 memory blocks. (if I understand well)
I've seen something talking about LSB and MSB concerning the address.
So I think, you might be talking about something that has to do with this. Is that right ?

But can you notice, on a previous message when I'm using Nick I2C Scanner on 2 different EEPROM, I got :
For the 24C02 :
I2C scanner. Scanning ...
Found address: 80 (0x50)
Done.
Found 1 device(s).

I've tested another one in SOIC package (Reference unreadable) and I get :
I2C scanner. Scanning ...
Found address: 80 (0x50)
Found address: 81 (0x51)
Done.
Found 2 device(s).

So, I deduce that the 2nd EEPROM was more than 256Bytes and needs an address on 2 byte (LSB and MSB)

Fortunately, we can see what happen on 2 examples. (2kB or more)
Unfortunately, the Write/Read sketch don't work for both !

I hope I'm clear enough as I'm a beginner and English is not my first language.

Many thanks for your help.