I have big problem with restore process in direct admin , after hours I don't know if direct admin still do restore the backup or not, would you please help me to know how could I monitor its process?
You have to look in the ticket manager and see if it created a ticket about the backup. It will either give you errors or say that it was successful. You can also look at the processes running on the server with the ps command or use top to see if you think it is still extracting. Usually you can see a process name like gzip which means its extracting things somewhere.
to speed up the restoration you can make the process less nice by either changing a value in directadmin.conf (if i recall correctly, i can give the exact steps to follow if you wish) or from the process manager.