How to burn HD videos with menu system onto DVD media?
Sorry to say this, but DVD does and will not support HD videos - at least not with menu and other DVD features. HD-DVD didn't survive on the market - Blu-Ray did. The problem is that the amount of data necessary to create a HD image is higher that the bit-rate of DVD-Format.

You can save various file formats on a DVD-ROM and some DVD players can play those formats. But "native" HD on a DVD is not supported. Some DVD Player can upscale certain compressed formats, but that will not show real HD.

See: http://www.dvddemystified.com/dvdfaq.html#2.3.2