Is it possible to slow down the video and to synchronize the video with the background music?

Do you have the suite ot the deluxe suite?

Select the video section you want to speed up or slow down and then click on the scissors icon (trim) adjust the speed from there. With V8, the icon is a clock with a pencil by it. After that the window that opens looks the same.

Please explain the second question. Automatically, no. You might want to try CineMagic if you are not too particular. There are themes there where the scenes change at different rates. Perhaps you can select a theme that goes with your music.