Hi Klara, I am a teacher here on italki, message me if you still want a teacher. Thanks.

Sometime teachers can't or don't adjust the times that they are supposed to be free, but if someone declined you without giving an explanation I would look somewhere else.

It means that they declined your request.

The green means the time slot is available. It will change color if the teacher accepts a request for that time slot. Teachers are free to decline a request. Sometimes they explain why and sometimes they don't.