If the probiotic bacteria have a food source, they can last a long time and even populate themselves. Is any sort of sugar or even protein source listed on the package ingredients? If not, you could add 1/4c of molasses per gallon (mix with warm water first to dissolve). Refrigerated, it should last perhaps a week or two. The molasses will feed the bacteria. It will likely last far longer than 2 weeks, but I'm just saying that to be conservative. I wouldn't worry about it going bad unless you end up with a very foul odor. You could even try to populate the probiotics by leaving the gallon container out at room temp for 2-3 days before using. If you try this last step, just be sure to use a plastic container with a tight lid and shake daily...gasses may be released and a glass container could explode.
For your second question...measure the contents of a full packet, either weight or volume, and divide by 4, to get the amount needed for a quart.
Want to make your own liquid probiotic for pennies? Try this:
Chop finely 1 head of green cabbage (regular or napa but not savoy)
Smash them in a metal pot with your fist or a rugged potato masher to release juices
Stuff the cabbage into a quart jar so that it's about half full, packed tightly
Fill the rest of the jar with chlorine free water
Cover with a rubberbanded cloth to keep flies out
Ferment at room temp for about a week at 70-80F or longer at cooler temps
Pick and toss any mold off from the top, the ferment underneath is fine
Strain and use the liquid in your chicken water
You can eat the solids or feed them to your chickens, it's full of probiotics too
Yep, the above recipe is one for sauerkraut, sans the salt. Chickens don't need that much salt, so regular kraut would be too salty for them. You could add 1/2tsp sea salt if you really wanted.