I read that arcgis saves all the processes in a log file, and I was wondering if I can run this log file and all of its processes in a free GIS software like QGIS.
you cannot run ArcGIS tools in QGIS. The log file you're referring to is a .txt file that says tool x was run on (date/time) and was completed on (date/time).
I am not aware of this. One thing you could do is check what was run and then replicate the same or similar tools in QGIS.