The phenomenon you mention is called Noncoalescence, and there are many beautiful experimental examples of it (see for instance [1],[2]).
Indeed, droplets of various liquids may float on the respective surfaces for extended periods of time prior to coalescence. The problem of explaining why this happens has been addressed by Klyuzhin et al. a few years ago, with some attempts to explain it better than had been done in the past.
I quote, from this paper:
When a droplet of liquid falls onto the surface of the same liquid, instant mixing is generally expected. However, even in everyday situations, small droplets can sometimes be observed to float on surfaces without instant mixing, for example, when droplets fall into sinks or during rainfall, when splashes create tiny droplets that may move swiftly across puddle surfaces. Despite such common experience as well as a number of relevant scientific studies, still, the concept of delayed coalescence remains counterintuitive.
A number of hypotheses have been proposed to explain the delayed
coalescence. In 1900, Reynolds proposed that droplets can reside on
the liquid surface because a thin film of air becomes entrapped
underneath the droplet. However, Mahajan later reported that water
did not form floating droplets at atmospheric pressure but that
droplets could be more easily produced at higher altitudes where air
pressure was lower, the opposite of what was expected from Reynolds’s
hypothesis. The positive effect of reduced air pressure was more
recently confirmed in studies of oil-droplet lifetime. Because
diminished air pressure should diminish the thickness of any air
cushion, these latter observations have seemed difficult to reconcile
with the early air-cushion hypothesis.
They then propose an explanation for this mechanism:
Recent results from this laboratory show an interfacial zone extending
down from the surface sometimes by up to hundreds of micrometers or
more, enhanced apparently by incident infrared radiation and also by
oxygen. The presence of a substantial interfacial layer could work
as an effective barrier that prevents instant coalescence.
A possible mechanism based on the presence of this interfacial layer
is illustrated in Figure 13. Before droplet and bulk come into
contact, both entities are presumed to have significant interfacial
layers (1), which prevent immediate coalescence (2). Once they touch,
the interfacial layers begin to dissipate (3). When the layers have
dissipated sufficiently, coalescence begins, and water from the
droplet begins to flow downward (4). As the water evacuates, the
droplet diminishes in volume, creating a narrower entity between the
droplet and the bulk (5). The pinch-off creates the daughter droplet
(6). The process then repeats, perpetuating the cascade.
According to this link sound (especially high frequency sound) is more attenuated in fog, because it is dispersed by the (billions of) air-water interfaces of all the droplets. This is one reason why a fog horn is a very low sound - low frequencies travel further, especially in fog. For echolocation you want to use high frequencies, and fog is more attenuating at those frequencies. Another site confirming this information is this one - slightly older than the other one. Of course one might wonder whether one article got its information from the other (it does look similar...).
Finally there is a very thorough (if old - 1953) paper on the attenuation of sound in fog in the Caltech library. Interesting diagram from this paper confirms that the attenuation of sound in fog is stronger at higher frequencies (for details of the definition of β see the paper):
Even with the question of attenuation - when visibility is reduced to 40 ft, echolocation will probably beat it handsomely at intermediate distances. There are a couple of other interesting things you can do to improve your ability to see in fog.
1) Yellow "driving glasses". These work because they cut out the blue components of light. When fog droplets are very small, light scattering is in the Rayleigh regime - that is, scatter probability goes as the inverse fourth power of the wavelength, and blue (400 nm) light is 16x more scattered than red (800 nm) [note - using round numbers...]. By cutting out the blue component, you reduce the amount of scatter that reaches the eye and improve the contrast. Skiers also use yellow "fog glasses".
2) Scanning light source. This is one of those magical things that ought not to work but does. With normal (flood) illumination, light scatters "from everywhere to everywhere". If instead you look along the line of (say) a laser shining into the fog, then the only scattered light you see is the light that scatters exactly 180 degrees back at you - which is a small fraction of all the scattered light. If you scan the light source and detection system in sync, and very quickly, you can build up an "almost scatter free" image. This raster scanning technology is used in some underwater search applications and can penetrate about 6 "attenuation lengths". As was discussed in the comments, this method actually works best when the viewing angle is not exactly 180 degrees - not only is the back scatter from the fog weaker (there is a curious doubling of scatter intensity that happens at exactly 180) but also, by looking at a slight angle, you are able to eliminate the back scatter from the closest fog - greatly improving penetration.
More recently researchers in Israel have come up with a way to image through thin layers of scattering material - as you can see in the link, they are also able to see "through fog" (although it was not clear to me whether their technique can apply to actual imaging in fog).
Best Answer
So there's two parts to this. The first is that the gaseous vapor in the air does not "want to be" condensed unless it has the appropriate pressures and temperatures around it. The bottom of a typical cumulus cloud is "flat" because the stuff that's falling down beneath this surface is re-evaporating while the stuff that's above the surface is condensing. In other words, clouds are a very non-equilibrium phenomenon; they look fixed and constant but it is very similar to how a candle flame looks fixed and constant: secretly we know that the wax molecules involved in combustion are always new ones from the solid candle-body, and the candle can only be sustained if that body is being consumed. Similarly, clouds are always part of a heat-transfer process from a warmer region to a colder region.
That would not account, however, for the "puffy" tops of these clouds. To understand those, you have to understand that when the vapor condenses into a droplet it releases its heat to the surrounding air, which warms up and therefore, since hot air rises, it feels a buoyant force and heads upwards. It "pulls" the droplet a bit with it, and since the droplet is small it has a high surface-area-to-volume ratio and this "pull" is actually relatively significant. That's what causes the droplets to fly upwards and create these puffy tops of the clouds, compared to their flat bottoms.
A fog is just a cloud that is formed at surface level. The basics are not so different and just require the wind to be blowing the damp air in a direction other than upwards. If the damp air comes into a colder space, even if it blows across the surface or up a mountain, then under the right circumstances it will form those low-lying clouds that obstruct visibility that we call fog. Again, the droplets still, as they form, heat up the surrounding air a little bit and this drags them upwards a bit, so that they seem to defy gravity. Unlike in the atmosphere, there is no surface that they will re-evaporate underneath, so they eventually just fall to the ground: this is why you might get damp when you're out in the fog, as this moisture hits you on its way down.