Fog/Mist = Visible moisture. Generally, you need clear skyies (can there be more than one?) so the land cools rapidly. As mentioned you get it when winds are light. If there is no wind you tend to see a very heavy dew. If the wind is stronger then you tend to see low stratus. Assuming light winds and a suitably clear sky, the coldest time of the day is about 5am, so the air near the ground can condense and you get morning fog. In the evening, the ground is likely to cool rapidly (more quicly that the air), so the air temp drops below the dewpoint and condenses causing evening fog. It is epecially so Spring and Autumn because the temperature range between night and day is highest.
Advection fog I am a little hazey on (pun intended). I see it as simply warm wet air getting shoved over something cold. Because the air needs to be moist this usually involved warm and cold sea currents rather than warm sea and cold land mass, because in the latter case the surface wind would blow out to sea. But I suppose the land could be a tad warmer encouraging the air in, but not warm enought to disperse the fog. Therefore it is usually seen at coastal areas or out to sea. I didn't think we get much of that round these parts, apart from a bit of Sea Haar and Fret along the North Sea coasts oop North I didn't think we see much of its ilk.
Haze = Solid particulates in the air reducing viz. The usual suspects are high pressure systems and/or inversions preventing the particulates from convecting away from the lower levels. Sometimes, I have noticed, it takes a day or two to build up. The conditions usually go hand in hand with light winds. When the wind picks up it is because of the onset of a front or the system moving away, thus releasing the crud, so the view that the wind blows it away is a little inaccurate (methinks).