If you are brewing all grain you will have to pay attention to your pH if you want clear beers. pH will give you a better cold break which will help with a beer's clearning. Also cooling rapidly can drastically help in the clarity. Irish moss or Whirlflock will help in clearning. Certain yeast are simply stubborn to clear, Chico (US-05/WY1056/WLP001) is one in particular. Gelatin or other fining agents will help dramatically. Biofine Clear is an excellent fining agent. But as mentioned, cold and time will clear all beers eventually.
Absolutely, without the oxidation added from the fining agents to boot!
Does chill haze drop with time? I assume so. But I guess I don't know for sure since I'm asking.