Acidophlius doesn't really kill off anything. It's just good bacteria. The way I understand it, the good bacteria gets into your guts and takes up any available space it can find. As bad bacteria die off, the good bactiera takes it place--so long as you have good bacteria there, ready to move in. I liken it to urban revitalization: good bacteria start moving in and then their offpsring move in close by and before long you have a much nicer intestinal area as the good bacteria just slowly push the bad bacteria out by not giving them anyplace to live and reproduce.
I don't know that acidophilus or any probiotics actually cause you to have more bowel movements by themselves, but if you are constipated because of bad bacteria, you should get better as the bad bacteria lessen. But the opposite is true as well: if you have diarrhea because of bad bacteria, getting rid of them should stop you from having diarrhea. Basically the good bacteria bring your system back into balance so you can have normal poops. Probiotics, like acidophilus, though, can cause excess gas, but the regular users of probiotics say that your body will adjust in a week or two and you will quit having the excess gas.
Probiotics will not do anything against parasites. If you suspect you have parasites, you have to see a doctor to get tested and to get very specific medicine to kill them. Antibiotics can kill bacteria, but it kills good and bad indiscriminately, so you have to be careful with them and make sure you take probiotics to help replenish your good bacteria or bad bacteria may set up residence.
Calcium is only one thing that will help your loose stools. Many people like to use fiber as well. Fiber, however, has to be added into the diet slowly since it can cause excess gas, but, as far as I know, calcium does not. I saw pretty quick results when I started taking a calcium supplement. But some people can't tolerate calcium, so fiber is a better choice for them. Some people just feel they need the fiber anyways and want to take it. And some people take both because they need both to get normal.