Apparently you call you master list of documents "List of Valid Documents" and this list appropriately identifies the current (and valid) documents which should be in use.
There is no need to stamp the documents VALID simply because you use the term in you master list unless, as Mark and Don have pointed out, that you state in your document control procedures that they should be stamped.
As to the second question, there is no requirement for having the master "List of Valid Documents" available on the floor unless you require by procedure that document users check to ensure that their procedures match the issue on the master list. If your document control practices are working correctly then you should have good assurance that the users always have the latest valid issue in hand. If your document control practices are not working correctly the problem will be detected in your internal audits and you can initiate corrective action. But, bottom line, do not implement a practice of stamping the documents to show validity unless you have the requirement specified in a procedure OR it is absolutely necessary in your work environment to ensure that document control requirements are being met.
