In my first QGIS project I have dozens of digitized layers that have spread beyond the contour and dem tile area that I started with. Please recommend how to safely expand or replace the dem and contour layers with larger ones in the project.
It sounds like you'll need to source some more data. There's no way to expand your DEM or Contours without actually finding data.
I'd suggest that you look into your local, regional, or national government spatial agencies. Perhaps search for open data repositories in your area.
If all else fails, there's a global elevation model at around 30 m resolution called ASTER, which will be available in your area: http://asterweb.jpl.nasa.gov/gdem.asp