Yes, mail continues to reach inmates in disciplinary custody. That channel stays open even when almost everything else gets restricted, which makes letters and postcards the most reliable way to stay connected during this stretch.
Phone access drops sharply once someone goes into the SHU. The standard limitation is one 15-minute call per week, and depending on the severity of the infraction it could be less than that or suspended entirely for a period. Commissary choices also get reduced, typically to hygiene essentials only, and contact visits are usually suspended for the duration of the disciplinary placement.
On how long he will be there, there is genuinely no set minimum or maximum. That answer is unsatisfying but it is the honest one. The lieutenant who wrote the incident report has significant authority over the recommended length, and the Disciplinary Hearing Officer sets the actual term based on the nature of the infraction, any aggravating factors, and the inmate's overall record. There is no legal cap on how long someone can be held in disciplinary segregation in most state systems, and federal facilities have their own framework that similarly gives broad discretion to facility administration.
What does move the needle is his behavior from this point forward. An inmate who is quiet, compliant, and gives staff no additional reasons to extend the placement gets out faster than one who continues to create problems from inside the SHU. It sounds simple and it is, but it is also genuinely hard to do when the environment is as isolating as solitary confinement.
Keep the letters going. They matter more than you might think when someone has very little else.