Thank you very much for your answers.
I am worried about alla the details because it is the first time I use KLM and I don't want to have any trouble with my trip.
Another issue that I have is that when I go to "manage my booking" it appears my e-ticket number but it doesn't appear my friend's e-ticket number.
Should I be worried about that?

P.S. I have received both e-tickets by e-mail but my friend's number does't appear in "manage my booking" option.

I also want to know which boarding pass should I scan to the drop-off luggage machine. Should I scan the boarding pass for the first flight (Athens-Amsterdam) or the boarding pass for the second flight (Amsterdam-Edinburgh) ?

Thank you again for your quick answers.