Firstly, I want to know is there any way that I can get the history steps back after closing a psd file and reopening it. I also clicked on take a snapshot in history option before closing the file, can it help in any way? Secondly: Is actually there any way we can save all steps of history, so when we re-open the file, we can get them back? Actually I duplicated the background layer once and did all the spot healing, clone etc on that layer only, and client wants all the steps to be shown to him and I have lost the history because I saved and closed the file but when I re-open it all the history steps were gone. Can anyone help?
I also clicked on take a snapshot in history option before closing the file, can it help in any way?
A snapshot is most likely the version of the document once it was opened. You can create a snapshot but it will not be an older version than when you opened the document.
Secondly: Is actually there any way we can save all steps of history, so when we re-open the file, we can get them back?
You can create a History Log, but that will only record the steps in text and you cannot revert a Photoshop document based on this log. You can do this under Choose Edit > Preferences > General (Windows) or Photoshop > Preferences > General (Mac OS). Click the History Log preference to toggle from on to off or vice versa.
client wants all the steps to be shown to him and I have lost the history
I think it is strange the client is requesting a step-by-step walkthrough of the changes you made. If the client requested this at the beginning, then I would think you have to redo all of your changes. If the client did not request this before you started. I would just say that you cannot do that and if they want it, they will have to pay more because it is an additional request.
You can read more about Photoshop History here: Undo and history