First, both of these will need for you do to the following.

In the Burn Screen Mode, press on the button that says "Edit" in the upper left section of the screen. This will configure the screen with many more options, both of which are necessary for what you are wanting to achieve.

Q1: Audio Playback for Menu

In the middle section on the right hand side, you will find a area that talks about "Design Page". In that areas you have the ability to manually alter the layout of the menu... something I really like about Movie Edit Pro.

The second option is for "Sound/Music", this is where you can add audio to the menu. Press the "..." button next the "Sound/Music" option and then select the folder that contains the audio you wish to load. It is that simple.

Q2: Video Background for Menu

This will work in the same way as the "Sound/Music". The third option for the "Design Page" is for "Video". Again, you press the "..." button that is next to the Video option and a new dialog will open.

This dialog has a lot of options, and not a lot of description, I have taken a screen shot of this, so you can see what I am talking about.

You load the video much in the same way you did the audio, you also have the option to set the start and end point... although I have never done this. Near the bottom, I believe by default it has a option selected that allows the video to loop, so as long as the menu screen is up, this video will play.

Now, other things to note after you have done this...

You can move the menu parts around on the preview monitor here in the center of the burn menu, this saying this is where you want this or that, they can be resized too. This is a ultimate feature to me, letting me customize the menu gives an extra personal touch.

If you notice, everything with the small boxes in the corners can be moves, and if you left click and hold the corners, you can resize.

I hope this helps, if not let me know I can go into more detail.