Poison and lab mice

There are 1000 bottles of liquid and exactly one contains poison that kills one hour after drinking. The poison can be diluted without limit. How many lab mice are needed within one hour to find the poisoned bottle?

If you may run two rounds of tests, how many bottles can you handle with one poisoned bottle? (Discuss both cases: mice can be replaced after death, and mice cannot be replaced.)

If two bottles among 1000 are poisoned, how many mice are needed?

With 16 bottles and one poisoned, how many mice are needed to identify the 14 safe bottles?