Will the 3DS play DS games?

Yes. The 3DS is fully backward compatible with the DS library of games and they fit into and play from the very same cartridge slot that the 3DS titles use on the system. About the only physical difference between the two is the small protruding tab on the top-right corner of the 3DS cartridge.

Since the DS games use a different resolution, how will they be displayed on the higher resolution 3DS screen?

DS games will fit the screen vertically, but will feature black bars on the right and left side of them in order to retain their original aspect ratio. This is similar to the way some widescreen movies are displayed on a 4:3 ratio television, only with the black bars on the sides instead of the top and bottom.

Will DS games display in 3D on the 3DS?

No. DS titles will not be displayed in 3D on the 3DS screen as they were not originally programmed to do so. DS games will basically look exactly as they do on your standard DS system.