An absent professor may pose a problem to your own research plans. It may also leave you without any guidance for a year. To be asked if you are prepared with a plan or design of your own. A research proposal and thesis are big projects. You should know ahead of time whether you'll get the guidance you need.
Bright people can disagree.
An essay you are proud of. Offer the portfolio to the professor during your meeting. We recommend that you read up and talk with other students about possible supervisors before you go to talk to them. Know about the research record and current interests of your potential supervisor. The department web pages have updates.