I talked with the vet, before I took her home. I will send one photo per week to the vet to see her leg. The vet put her in the box, and gave it to me to take her home in it. The vet told me to not touch her operated leg. The vet also told me that they have volunteers to arrange a transport from Szolnok to the vet, if I will need to take her back to the vet.
I successfully arrived at home with her. Approximately 185 km travel from the vet on public transport (bus, train and metro).
About the condition of my bird:
She lowers her left leg, but looks like she still does not (or rarely) sit on it, grip with it. I sent a photo to the vet on Facebook Messenger (the second photo in this blog post), and I wrote that my bird keep her claws in weird positions, and he told me that it is normal. She lowers her leg, but she does not put pressure on it.
I keep my Harris's hawk in the box in the upcoming days/weeks for her own safety.
I hope the best for her recovery.