Since you can't charge a lithium battery at faster than 1C (1 times the rating - so a 3000mAh battery can't be charged at a rate higher than 3000mA), and since charging is less that 100% efficient, about the fastest you can charge the battery is about 90 minutes from 9% to 100%. But since allowing it to drop below 30% is a bad idea (it kills the battery faster), and you should never charge it to more than 80% (that kills it faster too), you're charging from 30% to 80% at most - that's about 50% of the battery's capacity, so a fast (or rapid) charger should be able to charge a battery in about 45 minutes.
As for breaking, I don't know of anything that won't. Even the universe is going to stop working one day (see "the heat death of the universe").