Do graduate schools care if letters are confidential or not? In general, graduate programs prefer confidential letters. Admissions officials say that it displays more confidence on the part of the applicant if letters are "confidential" (meaning you, the applicant cannot see the letter). The Letter Service is required to indicate on the letter if it is confidential or non-confidential.
How do I approach potential letter writers? First, make a list of professors and/or supervisors who will be your best advocates. Then, set up an appointment to discuss your request in person. Do not make the request via email. Be prepared to articulate your interest and reasons for attending graduate school. Letters of recommendation are written strictly on a voluntary basis. The best approach is to ask potential letter writers if they are willing to write you a strong letter. If you sense reluctance or the answer is no, ask someone else.