Yup! At most institutions you need a faculty member to be the PI for a project, in which case you find someone vaguely interested in whatever area you want to research, propose the plan (under which you agree to do all the IRB paperwork, data abstraction, and abstract/manuscript writing), and then get to work. Sometimes you can latch onto a project with an organized PI where you might have a more limited, directed role, but all of my research projects since college have been me doing pretty much all the grunt work, and using my PI more for help refining ideas and processes. Having fellows, residents, or med/college students do a lot of the grunt work is super normal.
Nah, that's what electives are for. And if you're hoping to finish something significant by fellowship applications at the end of second year, you really should be getting started on something while you're an intern (whether it's a case report or review article to get your feet wet, or the IRB application for a bigger project).
Bear in mind that ACGME allows only a max of 3 months of research electives in a 3 year residency. And it’s unlikely that one would fit those all in before 3rd year starts.
