Honestly, you should just show up to the Physics Department. Come to room 1014, the main student hub for people involved in SPS and ask questions. If you're more inclined or even just more curious you should come to a meeting!
Meetings are held on the 10th floor of 726 Broadway in room 1067. Meetings generally go from 7-8:30 PM on Thursdays of each, but before and after the offical start of the meaning students are already participating in some sort of activity/hanging around!
Absolutely not! We welcome students in any major that is even slightly interested in Physics (Or not at all, we can change you I promise :D). The topics discussed in each meeting range from extreme theoretical physics, biology, math, linguistics, to just even talking about sodoku!
Ojectively, yes there are actually a lot of benefits. From staying up to date with events in the department, to various workshops, and hosting well respected lecturers. You also get to join an amazing organization with the sole mission of promoting physics across the country! From a personal view, you get to join an extremely welcoming community with equally amazing people who are willing to help you prosper in you academic career. All while making some of the best friends along the way :).
Even now, we have some big things that we are organizing for the department but an example of a major change accomplished by last year's E-Board was convinving the department to drop the GRE requirement for Graduate admissions. With SPS your voice is definitely heard!