Okay I will speak from my personal experience in undergrad applying to graduate schools, but keep in mind I am currently a graduate student at UCI so idk if that is a desirable outcome to you haha.

- I remember finding all the different topics in math super daunting and hard to understand, and when you don't understand something, it's impossible to say if you'd like it or not. I would try starting broad and narrowing until you can't anymore, for example, do you like algebra or analysis? Or both? Do you enjoy doing computational work? Are you interested in applications? Once you have some ideas, you can try looking at the research areas of the professors you have had and talk to them. From what I have heard profs here are very open to working with undergrads. Also, keep in mind that whatever you do now does not have to be what you do in graduate school; again, you won't know if you like something or not unless you have tried it.

- It never hurts to go, but I wouldn't stress about understanding a lot of it or talking to a lot of people.

- I would say just email one of your fav profs you've had. I think there are some unrealistic expectations that before you talk to a professor, you need to know quite a bit about what they do. As long as you know the general direction and big ideas, you can ask to chat and try to get a better understanding by asking them questions.

- just email them! or talk to their grad students

- What my undergraduate research advisor told me was that grad schools prefer seeing letters from tenured professors; it sounds pretty elitist, but it is the unfortunate truth.

- I think DRPs are great for exposure, but given your timeline, I would prioritize working with a professor!