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In order to use an SD card interface with the mini-breakout board I think you could take a look at the Schematic of the Arduino Expansion Board (SD Card - Section)
More documents in: Intel® Edison Documents and Guides
You can use an SD or USB drive for storage, you can also create your own image with different partitions. [Intel® Edison Boards — Board Support Package (BSP) User Guide]
About the A2DP connections; you can check the Intel® Edison Boards — Bluetooth* User Guide
Miracast, airplay.... Do you want to attach a webcam to the board and then stream video to another device? For example you can use gstreamer too.
Hope this helps.