As far as the main "essay" type questions go, they are usually listed on the website. The forms that the recommendation providers fill, however, are not openly available.
HBS Questions:
Recommender Questions (for both MBA and 2+2 applicants)
Recommendations must be completed online. The recommendation form includes the following four essay questions, along with other types of questions.
Please comment on the context of your interaction with the applicant. If applicable, briefly describe the applicant's role in your organization. (250 words)
How does the candidate's performance compare to other well-qualified individuals in similar roles? (250 words)
Please describe the most important piece of constructive feedback you have given the applicant. Please detail the circumstances and the applicant's response. (250 words)
Please make additional statements about the applicant's performance, potential, or personal qualities you believe would be helpful to the MBA Admissions Board. (250 words)