Some answers to your questions, based on my experience with wild sourdough starter in San Francisco:
- 70-80F is the ideal temperature range. Below that the yeast incubates very slowly; above it, the starter will tend to ferment alcoholically.
- Do not leave the starter in direct sun. UV light is a powerful sterilizing agent.
- An organic, cold-processed (i.e. stone milled) flour works best, because it will retain the maximum amount of its own wild yeast on it. Cheeseboard: Collective Works likes to start with rye flour and gradually add bread flour, but they don't give a tested reason for this.
- I have never heard of using fruit juice in a sourdough starter. I would be dubious about it; you'd be likely to end up with vinegar.
- Sugar is unnecessary for sourdough starters.
- Use purified water; chlorine/chloramine/ozone in tap water can kill your starter.
Finally, starters incorporating milk are fridge-only starters (as opposed to flour-and-water starters, which can be kept at room temperature if split frequently) which depend on the bacteria and lactic acid from the fermenting milk for part of their sourness. They can be effective, and actually a good choice if you live somewhere with weak/poor wild yeast. Note that you cannot transform a milk sourdough into a water sourdough, and using up 2 cups of milk every 2 weeks is more expensive than 2 cups of filtered water.
The difference between flour marketed as Bread Flour and flour marketed as All Purpose (at least in the US) is the type of wheat from which it is milled, and therefore the protein percentage in the flour, a p/l value close to 1 which gives proper plasticity to the dough, and a large enough falling number to allow long fermentations.
At least the US, all flour marketed as either All Purpose or Bread Flour should be suitable for bread making, although bread flour will permit greater gluten development due to the higher protein level.
The yeast or bacteria in a bread starter eat the starch (after it has been converted to sugar by enzymes present in the flour), which is the bulk of the grain, whether the wheat is winter or summer, hard or soft, red or white.
Also, the way the bag is labelled is as much a marketing issue as a technical issue. For example, in the US, King Arthur brand all purpose flour is nearly as "hard" (high in protein) as other common brand's (such as Gold Medal) bread flour.
Use either all purpose or bread flour, as you choose.
Best Answer
There are a couple of (potential) issues here.
First, sourdough starter doesn't involve store bought yeast, so I'm not sure I'd call what you have a sourdough starter-- I would call it more of a poolish or a biga. What makes it a sourdough starter is the cultivation of wild yeasts (this takes time, usually on the order of one to two weeks), but if you were to take care of and feed what you currently have for long enough, I would imagine that it would become a proper starter, although I would expect that to take more like months for the store bought yeasts to die off and be replaced with wild ones.
Second, two teaspoons of yeast for two cups of flour and two cups of water sounds like an awful lot of yeast. If I were baking something right away that called for that much flour I don't think I'd use that much. Related, thirdly, you don't mention anything about the size of your container, but I suspect its too small. Typically expect yeast related things to double in volume, so if your container couldn't hold at least that much it is too small.