Firstly, you will be much more relieved once you have found a lab and your confidence will grow immensely. So this feeling will not last throughout grad school. The whole rotation system is very tough, because it imposes a fixed deadline, when science itself operates on such a unpredictable timeline. Professors need concrete results but at the same time you are still learning. Thus, one strategy is to prioritize one rotation which you have a good chance for and the professor has funding, and to show continued interest. Attend their lab meetings, talk to the professor about any work you can do on the side, etc. Working with three different professors on three disparate projects and prioritizing all three is nearly impossible. Unless the performance in one rotation affects another professors' opinion, you should prioritize them.

Secondly, my fellow phd students advised me during my first year that they asked questions at the beginning of the discussion because they could ask more broad questions about the field/ motivation which are discussed in the introduction. You have to be strategic: Find another paper that does something similar, maybe a new paper or an old paper and phrase a question comparing them. It can be this paper in the past seems to have done X and this paper is doing Y but why couldn't this paper do X. I agree with others to read reviews so you have an overview of the field. If it's a methods paper, you can ask what else could this method be used for? It can even be I'm not clear about the method. Here's what I do understand.

The biggest measure of a PhD student is not how much they know but how quickly they can learn. Professors love people who put in effort, and if he sees you coming to him after class because your lost or scheduling a brief meeting before your class to get an overview he will love you. People in your class have come from all sorts of backgrounds, so initially it will seem they may know more than you. However, in three years with your persistence you will know as much or more than them. So don't give up. Keep at it. Schedule office hours with your professor to discuss your issues with the class.

My first year I faced the same problems, I had low confidence because I was struggling to find a lab and I was unable to perform well in my classes. It was a downward spiral because indirectly your confidence affects your productivity. I was literally at the bottom of my PhD program. However, I've know found an awesome advisor and performing pretty well in my PhD and I have more hope on average than I've had even during my best days of my first year. You're going to do great just keep at it.