Karyotyping? number of chromosomes/centromeres in each phase?

I'll assume you already know (or can look up) diagrams for the stages of mitosis and meiosis, so I'll skip as much of that as I can.

But before a cell goes through division, the chromosomes have to duplicate. They do this when the cell is in Interphase and the chromasomes are in their chromatiN, or relaxed state. But in order to keep them from having the DNA torn and damaged during the actual cell division, the DNA condenses into chromatiDs (<<-- note the change from the N above to a D) and forms the familiar X pattern. But the X is deceiving because it's not one, but two chromosomes joined where the lines of the X cross. Each side is a separate chromasome, identical to the other half. That's why these are named sister chromatiDs, they're like twin "sisters". Where the X crosses is where the two chromatiDs are held together by ONE centromere.

Now, if you just look at the diagrams from your book or somewhere online, you should be able to figure these out.