Can the ZED2 connect directly to a smartphone? Can I develop an android application to use with it?

No, the ZED2 cannot be connected to a smartphone. The ZED device is a passive stereo camera and it has a USB 3.0 connection. The ZED's can be used on several platforms, including standard PC
and also SBC (Single Board Computers) as the Nvidia development kit.

CUDA is required to use the ZED SDK because of the high computation power required to perform stereo depth elaboration using the resolution and framerate provided by ZED cameras.

As the ZED needs to stream both left and right images, it uses almost all the USB 3.0 bandwidth. The ZED SDK provides rectified images. 

So it is not a suitable device for using with a mobile smartphone. The same goes for ZED mini.


Additional Resources:

How does the ZED work?