You're fine. Yes, it is perfectly healthy to only get a period every three months. Yes, it was normal that you spotted for 10 days. That wasn't a "period" because you were on active pills, so it is called spotting.
Of COURSE you didn't get a period the second month! You never stopped taking the active pills (right?) so you never had a drop in hormones so you never had a pill-period. Periods on the pill are actually just "withdraw" bleeding, and not an actual period caused by the ovulated egg etc. Because you never had a placebo week, there was no "withdraw" period from the hormones and THUS, you didn't get any bleeding!!
You will not (normally) get bleeding if you constantly take active pills. That's the point of doing it.
Now at the end of the third month, you will take the placebo pills for their duration - I'm not sure how many placebos Yaz has. You may bleed during this time, but you may not!! It's OK. You're still safe.