What do you do when your car crashes through ice on a frozen River and is sinking? Take a selfie, of course!

Do they go on rivers? I’m not too terribly far from ice fishing country (I’m in Chicago), but I thought it was all lakes, and that there were ways of determining the relative safety of that (either by drilling into the ice and measuring it or … well … letting others go in front of you.) Do people typically drive on frozen-over rivers?

According to this, highs in Ottawa were below freezing between 6 and 24 January.

True, but the Rideau is a fast-moving river, ending in a waterfall where it falls into the Ottawa. (That’s why the early French visitors named it “Rideau”, which means “curtain”.). Ice build-up is more uneven for fast-flowing water, as others have commented.

There are photographs and video in the story linked by the OP. She’s like 40 feet away from the edge and you can clearly hear people talking in the video with no “rushing water” noise covering it up. I’m sure there exist rivers and circumstances where this is relevant, but it’s not for this one.

It’s harder to tell from the picture due to the angle, but in the video of her being rescued there’s clearly no stable ice near the car that she could have easily stepped onto.

No, they do not. Ice fishing on rivers is done near shore. That’s why I was a bit surprised she didn’t appear drunk. In the one video it looks like she’s driving 40+ mph.