What is the ruling on using the "Muhda" program, whose source is unknown, as is the method of obtaining it, especially since there are trial versions of it that become paid after a period? And how can the error of having already used it be rectified?

It is permissible to use the program available with the "patch" as long as it belongs to your friend. Nothing deviates from this original ruling except the presence of a strong indication to the contrary. If there is no evidence of infringement in using the program, then it is permissible to use it. However, if such evidence is found, you must stop using it. There is no sin for what has passed due to lack of knowledge.