Is it the same price to hire a lawyer for a written hearing after an appeal as for a court hearing?

In this case, the price will not change much, because the workload of defense lawyers is similar to that of trials without trial. The second trial of criminal cases is based on the principle of written trial, with the exception of trial in court;

as for the lawyer's fees, they belong to the fees for lawyers to provide you with legal services. The lawyer's job is not only to hold court sessions, but also to hold meetings, read papers, write defense opinions, and exchange opinions with judges and prosecutors. You can't judge the price just by whether you have a lawsuit or not.