is it possible to make all your editings in Sony vegas and use Encore 5.1 for dvd or blu ray authoring.
Yes.
Anyways, all default footages were recorded in PAL system and I edited and converted them to NTSC system with Sony Vegas Movie Studio HD Platinum 10.0 application.
So one possibility is that they are not correct NTSC. Make a very short test sample of the video and put it in an Encore NTSC project with no menu. Make it first play. Build to an iso image. You can post that so we can burn and test it.
If she was able to play the menu, but not the movie, that's good. If not, you can also post the psd of the menu for us to test.