Language immersion (Through the Academy int'l programs office and/or Olmstead foundation) usually requires to be in the language program, not on probation, and priority usually is given to GPA and class year.
Some programs are made by faculty, some programs are made by cadets submitting a proposed program for approval and funding. All trips are fully funded and cadets will have they meals paid for with some extra spending money as well.
There are other programs that are not language related like the JINSA program which sent me to Israel for 18 days last summer!
I also did go to Japan twice last year, summer for AF ops and spring break for an Olmstead funded immersion.