How do I know that my yogurt has live and active cultures in it?  I used store bought organic Greek yogurt with live and active cultures as my starter, and it turned out beautiful and thick,but I'm making it to replace taking probiotic capsules. In all my studying beforehand I never found a conclusive answer as to, HOW do I know if the yogurt bacteria is in it? 
The fact that you made the yogurt is proof enough. Your yogurt has live cultures.   In principle every yogurt is a colony of bacteria living in milk. When you make new yogurt, you are establishing a new colony, using the starter as "colonists" who then take over the new milk. The result is a lively ecosystem of bacteria.   Companies nowadays optimize food for long storage time, and frequently also for some blandness. Since a lively colony can go more sour with time, some of them actively go and kill the bacteria after the yogurt has been made. This stops the yogurt's taste from changing.   The reason why people warn you about choosing "live cultures" for homemade yogurt is that, if you happen to pick a storebought yogurt with killed-off culutres, they won't be able to colonize your new milk. Instead of yogurt, you will end up with spoiled milk, wasting time and food. They don't mean that you will make somehow "dead yogurt" from a dead culture.  