i want the user to be able to check the status of the document in the workflow as the document move from one to another to approve it, so the initiator cant see the updated done on document.
You can utilize Business Processes for to do that. In the workflow you would wrap the activities in a Business Process Step activity and you can set it to give the user instructions and resolutions. It will also track where it currently is in the workflow and how long each step took or is currently taking.
Here is a link to the help documentation.
but when the initiator start the process the document move from its folder to the another user folder to work on it. but the initiator have no access to the user folder. so how can i make him see what updated done on document and fields.
In the workflow when it moves to the next person, have it create a shortcut to the document in the initiators folder. This will allow them to always be able to check on it. At the end of the workflow you can also add an activity to have the shortcut removed.