The starting rating depends on a couple of things. In the old days, everyone started at 1200. Now, with the apps and v3 of the website, new members can choose a skill level that will assign different initial ratings.
The easiest way see the rating changes is on the website. That said, it looks like you must have your app set to unrated games. You are correct and your rating is the same as it was when you started.
When you create a challenge, next time don't just choose the default option. Use Create Challenge and toggle the Rated Game option to on (should be green and to the right).
The setting is sticky, so if you use the default challenge option it will remember what you chose last time. If you ever want to go back to unrated you'll have to do the procedure again. That process only impacts the seeks/challenges you place. If you accept another player's seek, that will be whatever they set it at.
My rating is 1000, but it looks like everyone starts at 1200, but I've always been 1000. I've played a number of games and win a few, I know some were unrated, but can I check to see after the fact? I'm using the iPhone app and can't figure out how to see if they all were. I'm just wondering why my rating doesn't fluctuate at all.