The display lights up, but I cannot get it to show any letters. I´ve tried both the A4,A5 and the dedicated SDA,SCL pins - but no I2C scanner code can identify the I2C device and address and no code works for showing characters no matter what libraries used.
Lots of Retailers deliberately lie.
In this case it looks as if the Manufacturer assembled the wrong chip and the Retailer did not realise that she had got some faulty items.
I would have a full and frank discussion with the Retailer. Get a replacement immediately i.e. LCD with backpack.
In case you did not realise, the PCF8591 is a DAC / ADC chip. Completely different function.
But a I2Cscanner should find it. Are there pullup resistors in the SDA and SCL lines?
Not really. The photo shows a familiar I2C adapter board with a circuit designed for a PCF8574 series chip. These chips have the SCL and SDA connections on pins 14 and 15.
If the board was actually populated with a PCF8591, which has its SCL and SDA connections on pins 10 and 9, then the scanner will obviously not detect it.