At a high level, no it's not really that relevant. Since the frames are (probably) all submitted to the same command queue, there's no GPU parallelism going on here, so the number of buffers doesn't really matter.

For a full answer on why you might want more buffers, check out this other topic:

http://www.gamedev.net/topic/679050-how-come-changing-dxgi-swap-chain-descbuffercount-has-no-effect/

You should have one more buffer than the number of frames that you queue, since one of the buffer is the one that it's been presented. So for a 3 buffer swap chain, you should queue up to 2 frames. That being said, queuing 2 frames should be more than enough (you want to keep your GPU busy but also to have a reasonable latency).

And for that error, if you are requesting each frame the right buffer, it should not happen.

The only reason for more buffers is to queue completed frames. And the only time you can queue completed frames is when using VSync. If you're submitting all of your frames serially, then buffer 0 gets off screen the same time buffer 1 gets on screen, and frame 2 can start writing to buffer 0 with no delay.

Though if you're using FLIP_SEQUENTIAL/FLIP_DISCARD (which you are since you're asking about D3D12), using sync interval 0, and not using the ALLOW_TEARING flag, then it makes sense to have more buffers, since you want to be able to queue completed frames here too.

In Present(). It's the first parameter.