A seed mix is fine as long as it is properly balanced for the needed nutrition and protein a Hamster requires. The bad side of a seed mix is the Hamster can pick out the seeds they like and leave others which then can make the food unbalanced for them. I make up a seed mix but I also feed a block food too. No new seed is given until the blocks are gone. This gives them a balanced diet with a treat like diet too.
Now on Fresh Vegetables you need to feed it very slowly and in small amounts to begin or it can cause intestinal upset and lead to a Wet Tail like symptom which if left could cause death. Also any fresh Veggie needs to be thoroughly washed to remove any fertilizers or chemicals applied to it. Fresh Broccoli and Cauliflower are great ones to feed to Hamsters. Not sure why they said to not offer fresh Veggies unless they have had a hard time with them with the store Hamsters.
I also would like to welcome you to HC and will look forward to seeing your Hamster and learn more about your life in Greece with a wonderful Syrian Hamster.