Hi Costis,
We have many users of KonaKart who use non-Western characters so we do know that it can support this.
Invariably the problem will be with the database configuration.
I just made a change to the configuration on the database being used on our demo application to ensure that UTF-8 is the default/server character set (evidently it's not enough for just the database to have utf-8 encoding).
You mentioned that you could not save Greek characters in our demo app earlier... In the screen images below I have saved some Greek characters, and some Chinese for good measure (one is from the Welcome Mail that is sent and another on the Account Information screen). (NB. I copied and pasted the Greek and Chinese so I'm not at all sure what I've written; I hope it's not inappropriate language :-)). Perhaps you could try to do the same and see if you get it to work this time?
I suggest that you check your MySQL configuration again and ensure that your encoding is defined correctly... I added these lines to my.cnf which seemed to do the trick for me:
[client]
default-character-set=utf8
[mysql]
default-character-set=utf8
[mysqld]
default-character-set=utf8
character-set-server=utf8
Kate