I cannot answer all your questions, but I caution you against thinking Greek life will be the same at every school. What it costs, whether or not it's possible to balance its requirements with those of a competitive sport, and the priorities of the school's social life will ALL vary with the school.
Very large schools, those with sports teams that take over fall semester, schools in the American southeast, *in general* are very competitive and the fact you're here for only one year could play strongly in your selection or non-selection. Smaller schools, those which are not often mentioned on sports-news segments, more specialized schools have a different vibe, and are more likely (note I am not in any way declaring this universal) to want the experience of a sister from another country, or who will spend only one year here.
Recommend you do some searching to see which American sororities have alumnae chapters in UK; to have an alumnae group once you return to UK might allow you the continued sisterhood many of us feel for decades after leaving college. Then see which of those groups are present at the campuses you consider.
That's only part of the entire equation. Best of luck to you.
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