Pretty much SOA; most end-to-end systems use these spectrograms on short time slices. The alternative is mel-frequency cepstral coefficients, which are used more in GMM-HMM speech recognition than for DNN.

What's the difference between the false-color frequency spectrum image and the frequency spectrum itself? Assuming that there's one horizontal pixel per sample, one vertical pixel per frequency bin, and that the color spectrum encodes the intensity to sufficient resolution, I'm not sure there is any difference.

The bitmap is just a convenient representation of a two-dimensional array, and PNG is a convenient compression library!

CNN on spectral images can work well. But most SOTA uses LSTM for speech recognition

That's right. This is not state of the art. LSTM is good for sequences and sequential data (like audio). But with the approach hereby described, prediction can be done in parallel and asynchronously. Which is something ;)