When you mix it, you're bringing everything to the same temperature, and if the amount of heat in your mixture isn't enough to bring all the ice up to 0C before all the water freezes, you're going to get a block of ice.
You could be careful about it, and figure out the temperature of your ice and your water, and get the right amounts, and perhaps even use warmer water (or warmer ice). But you can also just use less ice per water, and that's easy. Simply start with water and add ice, blending as you go, until you have the amount of ice and water that you want, stopping before you add so much that you just get solid ice. Once you've done it once, you'll have an idea how much ice and liquid to start with.
I don't really see why you'd bother lowering the freezing point. 0C is plenty cold for human consumption, and you can just as easily just use more water and less ice. If you do add things for flavor like alcohol, sugar, or anything with fat (e.g. dairy) then you will end up lowering the freezing point, and possibly making it softer when it's almost frozen, but this doesn't really affect the fact that you want to get it to the ideal temperature by controlling the temperature as you create it.
(Note that a smoothie is basically an ice slurry, with a lot of other stuff in it, and they're made just like this - blended with an amount of ice that can't freeze the whole mixture.)
Traditional pickles made with brine and vinegar are very hardy, and where used in the days before refrigeration to store food over many months
The secret is to only use a very clean utensil to remove a single daily portion from the main storage vessel, and otherwise keep the main storage vessel tightly closed and in a cool and dark location
With modern pickles, who knows? Read the side of the jar, if it seems to have a decent amount of salt and/or vinegar it should be just fine
If you haven't put dirty utensils or your hands in it, it will last a long time (weeks or months, depending on the ambient temperature level)
Otherwise, just keep them in the fridge :-)
Best Answer
If you have a clean glass pitcher, the length of time we're talking is months, as mentioned by Tom's answer.
I think you have a few questions that I can clear up:
The bubbles that form over time are dissolved gases. From the faucet (or pitcher), the act of pouring will force some air into the water. Over time, it will warm up and you'll see bubbles form along the glass. This is absolutely harmless.
Flies laying eggs? Well, I wouldn't leave a glass pitcher out and uncovered, but I highly doubt this. Flies want to lay eggs in places where the hatching egg can live. For example, trash, spoiled fruit, the gunk in your drain, etc..
Chemical reactions with dissolved ions? Since most water in the US is fluoridated, there will be some very slow etching of the glass by fluoride ions. The amount of this will be very, very small, since it's a slow process. I think you'll easily be safe over the timescale of days to a week or two.
So what happens to water left at room temperature over a few days? Mainly the dissolved gasses come out. I find this water to taste "flat" even if I cool it again. But there's not much that will happen to the water.
More than a few days and I'd suggest making sure the water is capped or closed to avoid dust or other things falling into the water. Maybe find a closable glass container?