I have not done a sourdough starter, but my DM used to have some-the same one for years (don't know if she made it herself, though). My sis has one that a friend gave her-so no help there...but....I DO make my own wine, which involves alot of the same principals and those little yeastie beasties.
My take on this:
You can make sourdough with just flour and water.
If you let this sit it will attract wild yeast. Here you take a chance-good yeasties or bad beasties. No way to tell what you have captured. If you add your own yeast-VOILA-you get exactly what you want.
Adding sugar (or some other sweetner-honey, molasses, syrup, jelly, etc.) would speed up the yeast multiplying process.
Warmth speeds up yeast (but too hot will kill it-shouldn't get over 100 f), cold will slow it (IMO-40 to 50 would seem to be optimal for storage, thus the fridge). For long term storage you could dry it like Westie described or toss it in the deep freeze.
Once ya get them little yeastie beasties in there ya don't want to let it sit uncovered. One of the byproducts (like Westie described also) is alcohol-winemaking, remember? Well, alcohol attracts other bad beasties-mainly the dreaded vinegar fly-YUCK! So keep it covered-but not tightly, cuz the other byproduct-carbon dioxide-will blow the lid off! A piece of cloth and a rubber band are perfect.
Feeding the starter? If it's in the fridge it should need fed very little. The freezer or dried-not at all-until you're gonna use it. Sitting out-depends on the temp and how fast the fermentation is going. A fast fermentation will produce more alcohol and at too high an alcohol content yeast die. Basically, the thing they produce kills them-nobody said they were very smart. Therefore ya have to remove some and add some to lower the alcohol content.
I'm sure I forgot something or another. If anything isn't clear just ask away.
Hope this helps.