1. Should I first use PrePro to edit raw footage, then go to AE to add effects?
2. How far should I go with editing a footage in PrePro, just cut each scene and make them match the music? no any effects?
Yes. Also allow your clips to have "handle" that is keep frames at the heads and tails that may later be used for transitions.
3. Then what if the effects added in AE changed the Sync previously done in PrePro, how should I go back to PrePro?
You render the clip in AE and replace it in Premiere or use Dynamic Link. However, if you already used DL to gor from Premiere to AE, that precludes using it to go back. It's strictly a one way process at this point, so rendering everythings is better (and more performance friendly for your machine).
4. Do I need to export video file with audio for AE, if not, how can I make the effects match the music in AE?
As long as the durations match, you can use separate audio files just as well, but of course if you already timed your clip, it makes sense to at least create a reference clip with emebdded audio for AE work.
1. what format should I choose to export from PrePr for AE use?
Some tutorial said that is better to use raw footage in AE, because of re-compression will reduce the quality (pixel) of the video, since I guess AE will do another compression when rendering the video
AE supports the same formats as Premiere Pro, so you would simply use the footage "as is" and not export an extra version. AE will just as happily create a composition from a PPro sequence no matter whether the footage is AVCHD or something else. given, that most source formats already are compressed, it is also a moot point on some level - there is no way to apply effects to compressed footage without recompressing it fully, so it will always not look as good as the original.
2. Is the work in AE will be the "Final Processes" for moving on to Encore? Then what format should I choose to render?
A DVD is always MPEG-2 at the proper SD resolution, a BluRay Disc can accomodate MPEG-2 HD and H.264. Whether or not it makes sense to encode straight from AE is a matetr orf preference and specific requirements for any given project, but it's possible. Please look up the exact fiel format requirements in the Encore help files.