In the source code of QGIS, I see a lot of QgsDebugMsg lines.
What should I do in order to show it when debug/run my standalone application in Eclipse PyDev?
I do not know what you mean for "show messages in eclipse-pydev".
Generally speaking, as you can see in the code, QgsDebugMsg is a define that use QgsLogger, and QgsLogger documentation says:
http://qgis.org/api/classQgsLogger.html#details
that you can use QGIS_DEBUG (level 0,1,2,3) and QGIS_DEBUG_FILE env vars to generate log file