If it had stopped anytime in the recent past we probably wouldn't know about it. We just have no reason to believe it would suddenly stop doing what it's been doing for 13 billion years. Kind of like gravity. We don't know if gravity is going to turn off tomorrow, but we have absolutely no reason to even consider that it might.
Yes, but, the information becomes less ancient as distance decreases. The expansion rate of the universe is deduced as a function of time. The Hubble constant scales smoothly across the history of the universe. That does not prove expansion did not suddenly halt a handful of millions of years ago, but, is viewed as highly unlikely.