Vinyl player emulation on Arduino
I have no experience with this particular type of application but my guess would be that it all depends on your available RAM and what sort of features the codec has for directing it to the buffered data in RAM. So when you scroll forward your code would tell the codec to skip some buffers in RAM. But meanwhile your code would have to anticipate what buffers will be needed and pull them from the SD card. So you need a good algorithm that can anticipate what parts of the sound file will be needed. To play backwards you would just need to reverse the data in each buffer. To play slow, it might be as simple as changing the bitrate of the CODEC to be too fast and thus the audio will sound slow.

But the first thing you would need to do is identify the chip on the audio shield used to actually convert the sound file to digital audio and carefully study what sort of control you have over how you feed it data. It might have a routine that can access a file on the SD card directly but of course that would be of no use to you. It probably has lower level routines that work on buffers. You would need to explicitly tell it to play individual buffers in RAM. Then it's all about getting the right buffers in RAM.

You might not have enough RAM to do this actually. Before you get carried away, you should figure that out.