The Emmanuel interview is over 10 years old, but the questions used were ones that were used at interview a year or two before that (so were "actual interview questions"!).

Each question went further, so depending on the candidate it had the potential to get significantly harder. The purpose of the interview is to see how you think and react to new ideas etc, so they are trying to get to something where you have to think (i.e. not just regurgitating A-level facts and techniques). I think it's also worth noting that questions that seem fairly easy sitting at home watching a video would probably seem a bit more difficult under the pressurised environment of the interview room.

Each college does it's interviews slightly differently, but the make up of this one (a few minutes talking about your school, or things from your personal statement to make you feel relaxed / warm you up, then into the maths) is fairly typical.

One of the things to take away from the video is that "Lydia" talked through what she was thinking, and used the paper to sketch ideas. The main thing to avoid is just sitting there saying and doing nothing if you are asked a question that you do not know the answer to straight away (although a bit of a pause before replying is ok). By talking through your thoughts, and using sketches/noting down equations etc. you can demonstrate your problem solving techniques.