If you want to verify whether this is graphitic carbon, check out Raman spectroscopy. All forms of graphite-like carbon as well as carbon nanotubes have a band around 1600cm-1.
If it is possible for you to explain the heat treatment parameters, i.e., time and temperature, and the complete chemical composition of the studied steel it would be more easier to discuss about the observed microstructures.
However, from your current information, my comments would be as follows:
1) Considering the studied steel as a plain carbon steel, since the carbon content of it is around 0.54 wt% it is a hypoeutectoid steel. During an intercritical heat treatment of a hypoeutectoid steel, prior austenite and proeutectoid ferrite are stable constituents as inferred from the Fe-C binary phase diagram.
2) During quenching from the intercritical annealing temperature, and if the quenching rate is "fast enough", the prior austenite would be transformed to martensite and the final microstructure at room temperature would be martensite and ferrite.
3) From the second microstructure, the white, flake-like constituent seems to be the proeutectoid ferrite (ferrite) that decorates the prior austenite grains boundaries during the intercritical heat treatment, and the brownish matrix is the martensite phase that forms during rapid quenching. I think if you increase the etching time you may see the substructure of the martensite phase.
4) There are very small particles dispersed in the martensite matrix, which I can hardly discuss about them with your current information. However, they might be undissolved cementite particles originating from the initial microstructure (probably ferrite + pearlite). Depending on the intercritical temperature, if the annealing time is not enough the cementite layers will not dissolve completely in the austenite and such a microstructure will appear after quenching.
5) I recommend you to measure the hardness of the quenched samples, which helps you to better characterization of the microstructure by comparing their hardness with the hardness of full martensitic sample.
6) There are some other phenomena occurring during intercritical annealing and quenching of plain carbon steels such as auto-tempering of martensite or epitaxial ferrite growth, which you may need to be aware of for advanced characterization of the microstructures. I think the book "Steels Processing, Structure, and Performance" written by Prof. George Krauss can provide more and detailed information for you in this regard.
Microstructure showed in top photos is essentially a fibrous primary lath martensite
as BCC iron containing C-rich phase precipitating in quenching.
It would take lots of time in explaining and understanding and that I do not have. However, just do one thing to get hold of book - "Steels - Microstructures and Properties by RWK Honeycombe - a mastro of ferrous metallurgy. Try to read it and you will learn lot. All the best,
Based on the heat treatment and optical micrographs presented, it appears to be ferrite (light colored etched) + martensite (dark colored etched). Since the intercritical temperature is only slightly above the lower critical temperature, hence there is less of martensite.
You may try Lapera etching to cross-check the dark phase. Higher magnification SEM will almost definitely confirm. As earlier suggested, Raman spectroscopy can help resolve the presence of graphite but I suspect it not to be graphite due to unfavorable kinetics.