The process is likely to be different in different places (even within the same country, or university), depending on the person interviewing you. I currently work in Germany. At the University of Bonn, the topology group interviews candidates together. The interview consists of a 30 minute presentation by the candidate, usually on their masters thesis, followed by 30 minutes of questions. The scope of the questions is informed by the presentation -- the first half is usually based on the talk, and the second half on general questions in topology, of the type we would like the candidate to already know before starting a PhD position. Sometimes we ask the candidate whether there are specific topics they feel most comfortable with, but usually this is clear from their application. Yes, we do ask the candidates to solve math problems.
Even within my university, the process varies from group to group. Others might just have a quite informal (virtual) conversation with the candidate, the talk component might be unique to the topologists. The length of the interview is highly variable.
My advice to you:
Ask the person who invited you to interview what the planned format is and what you should prepare.
Regardless of the answer, be prepared to answer questions about your masters thesis, your general area of research, and the direction you would like to pursue for your PhD.