The answer kind of depends on what you want to do and why you are taking the year off. You're kind of asking lots of questions that are basically individualized questions that you need to figure out on your own. You say you want to do a fellowship (in what?) but you are taking a year off with no set goals it seems other than to make your application more competitive. To be honest, that is unlikely to happen in a year, especially since you don't know what you're doing.
A lot of times when people take a year off they do it for specific reasons, and have already lined up a plan. I would think a lot of programs would ask you why you are taking the year off and what you did with it, and why. You shouldn't do research just to do research. If you have no experience in path but want to do path it would obviously be best to get some kind of experience in the field. Why do you want to get into the most competitive program? Is your goal to just get into a path training program? Do you want to do academics? Or is it just to get into the best program so you can get the best fellowship and make money? Things change based on goals. For many people who want to go into private practice, the choice of program is not hugely important.
As a foreign grad, your best factors in your favor will include board scores, letters of reference, and experience within the field. Research is unlikely to help unless it is significant.