1. house a certain number of shrimps that can live long enough to: breed and maintain population despite the imminent deaths from the Barbs? If yes, how many?
Possibly, but I saw ditto on setting up a separate tank and once you get some offspring in there that are rather large, you can then try introducing them into the community tank.
2. How long cherry shrimps live? (let's say they managed to avoid getting eaten)
Typically 1-2 years
Amanos can live for 10+ years potentially, but their offspring cannot survive in fresh water.
3. How long does it take for them to breed after obtaining adults from the shop?
As stated, varies.
4. How long does it take for the babies/fry/whatever you call em, to grow old enough to breed themselves?
Juvies (babies) may take 3-6 months before they start reproducing, if conditions are good.
A good question is... do you know the GH, KH and TDS of your water?