Which homeopathic "medicine" are you referring to? The disadvantage of homeopathic remedies is the insufficient amount of data and research that is reliable. There are numerous of claims from people stating that such remedy has "cured" a particular ailment. Perhaps there is some merit to such claims but keep in mind that each person is different and will have varying degrees of results. Be sure to collect information on the particular "medication" you plan to consume and make sure that such information comes from a reliable source, not only from the manufacturer. Also be sure that the ingredients will not interfere with current medications you are taking. There are serious interactions that can occur despite the homeopathic remedy comes from a natural source.
Homeopathy is crap - there is not a single molecule of active ingredient in it.
Water has no memory - if it did, how could it have selective memory? It would remember fish poop too.
I'm not sure what you mean by the rest of your question.