Where to find a waypoints/fixed points, navaids and airports database?
Nice question. There are several ways how to get these information.


http://www.fallingrain.com/: free to use, no registration needed. World database of the airports and waypoints. From these information you could easily make DB for waypoints.
EUROCONTROL EAD (https://www.ead.eurocontrol.int/eadcms/eadsite/index.php.html): free to use, registration needed. Big advantage - real and up to date information for all ECTL countries. But a bit difficult navigation.
JeppView (http://ww1.jeppesen.com/): very expensive SW, but the best in this time. You will find there all information which pilot needs. But it is not real database.
Garmin for pilots (http://www.garmin.com/en-US/explore/intheair/): another not free SW, very similair to JeppView but lightweighted.
NAVIGRAPH (http://www.navigraph.com): Great DB of all things which you need in FMC. But I guess that they have it just for flight simulator.
OpenFlights (http://openflights.org/data.html): free DB of airports, airlines and routes. You could downlod all data in one file :-)