The follow up for an appellate remand is normally a few weeks to 3-4 months. It depends on the prosecutor's office to set the pace based on their caseload.

Appeals require a clever lawyer that can find a mistake in the trial. They are generally a long long shot of even getting heard much less overturned.

The court appointed lawyers work for the Public Defenders office and you don't get to pick, they "appoint one". The inmate will have ample time to speak with, meet with and assist in the construction and the filing of the appellate document. Good luck!