You can use SolidWorks explorer to update the drawing references. Select your drawing in SolidWorks Explorer, then go to the "References" tab. Right-click the part in the list and select "Replace"
Yes, you can do that in SW. There are at least two different ways. Do a search here for "change drawing reference".
Yes this can be done in SolidWorks. In SolidWorks, choose to open the drawing file you wish to associate. In the bottom left corner of the open dialog box click on references. Click on the part name that is currently referenced to the drawing. This is launch a browser dialog. Browse to the file you want the drawing associated with and select it. The reference dialog box should now show the new part name in green indicating it is being associated.