I would like to have an opinion about microscopy techniques to distinguish between folded and unfolded protein molecules belonging to a same or different proteins.
Am not aware of a microscopy technique that would do the job in a straightforward way, but EM might be an option. As an alternative I would recommend using a technique like CD (circular dichroism) which can discriminate folded from unfolded proteins.
Another nice microscopic technique -very useful to explore microscopic pathways in protein unfolding- is single molecule FRET, with an adequate selection of the donor-acceptor pair.
It is a good practice in protein unfolding studies to combine the information from several techniques. As mentioned by Guus, far UV Circular Dichroism is one of the reference techniques. However, it does not always work, e.g. it is not useful to distinguish between native and SDS-induced unfolded states in membrane proteins.
regarding CD- you cannot distinguish between folded and unfolded. You can try to extract them from the CD spectrum using a good model
FCS - the fact that unfolded and folded have different translational diffusivities does not mean that these a different enough to be observed as different species with different diffusion times (it is actually ridiculous to try to shoot for 2 diffusional processes with a difference of a factor of x1.5 between them in a logarithmic lag representation).
FCS - FCS is nice of the folding-unfolding transition occurs at least a 100 times faster than the translational diffusion time (to have a time separation between the two processes) and if your dyes conjugates are designed to change fluorescence when changing from folding to unfolding (and vice versa)- FRET, PET, PIFE, etc. Beware that inthis case, the folding-unfolding dynamics may be mixed with photophysical phenomena such as dye photoblinking.
smFRET is the best way to go if you want to distinguish between folded and unfolded. This is true,of course, as long as the interconversion between folded and unfolded forms occurs at a timescale of the diffusion time through the confocal vol. or slower. If it is a fast folding protein (see works from Munoz), in smFRET you will observe,many times, a single FRET population at transition mid-point which is simply the protein averaged-out FRET efficiency of both folded and unfolded states. Beware of the possible effects of the large dyes being used in smFRET (large hydrophobic systems that usually make up the fluorophore part of a dye) with the unfolded state (artificial promotion of a hydrophobic collapse). Also make sure the protein you are studying is sufficiently larger than both the dye sizes.