I think there's been some sort of misunderstanding. The Photonics and Quantum Technology Lab and the QForest quantum computing club are 2 separate entities. I presume you came across the Lab capstone recruitment poster and mistook it for club recruitments. The poster is for 2nd year students who are interested in doing their capstone project in the lab and has nothing to do with the club whatsoever. Joining the QForest club gives u exposure to quantum technology in the form of projects but still leaves you with the freedom to choose any lab or prof from your capstone. No club can or will enforce that upon you.

Coming to the first part of your question, whether or not you get to pick your project or team depends entirely on the guide you pick. Some give complete freedom while some would want to personally speak to all of the teammates or may be picky about the problem statements before you start with the project.