How to slow down playback

You can't slow down audio playback without changing the pitch. 

Within reason, you can open an audio file in a specialized audio app like Adobe Audition and change the duration of an audio clip while maintaining the pitch. There are limitations. You can't extend two seconds of audio to four or six seconds without a pitch change, but you can change two seconds to two and a half. 

If you need to match action to movement and the tempo is very fast, it's a good idea to use the waveform (keyboard shortcut - press the 'l' key twice and drag down the bottom of the waveform to give you a better view) and then line up your keyframes with the peaks. Some prefer Rectivied Audio (set in the Timeline menu), and others prefer the normal waveform display. 

Here's the problem you can run into when trying to sync movement with audio. Making a cut or a major move right on the beat is often the wrong approach. Anticipation plays a huge part in the timing of any edit. Sometimes making a cut or a move just before an audio hit gives a more dramatic effect on the viewer, but sometimes, making the cut or the move just after the audio beat is stronger. It all depends on the sound and picture interaction. 

Converting Audio to Keyframes will give you a level on every frame, and you could use the graph editor's Value Graph to see exactly where a threshold is being crossed, That would be more accurate than just using the waveform, but the anticipation or reaction to the sound for the most emotionally engaging edit is still not always going to conform to the exact beat of the music. 

My suggestion would be to use the Graph Editor/Audio to Keyframes tool or just the Waveform (LL) to set the initial keyframes, then watch 2 or 3 seconds of the edit at a time and see how it feels. Adjust the timing of the keyframes by dragging them left or right in the timeline until the drama you are trying to create seems to work best. You won't see any of that if you preview at a lower frame rate, even if the pitch of the soundtrack is correct. 

When you think you have it, watch longer previews. When the longer previews work, step away for an hour or two and take a fresh look at the cut again. I've used this workflow for my entire career, and it applies to everything from feature films to documentaries to music videos. I've done a bunch of them. Anticipation and reaction is a critical part of all editing and the perfect cut is not always right on the beat.