Having lived in California most of my life, I've been through a number of large earthquakes.
While they can travel quite a ways, it's on the order of a few seconds at most. I've been on the phone with people or listening to AM radios stations and will hear someone say "I think that was an earthquake" about the same time I feel it.
True. There are many small earthquakes every day, but they are not felt, do no damage and don't warrant making the news. Unless it is a "swarm" of earthquakes, they don't talk about them.
The delay is due to the processing of the information. A seismograph will tell you there was an earthquake and how strong it was at that station. What the USGS does is to take data from many seismographs and plot the epicenter and magnitude. That takes some time.
You won't hear earthquake warnings. I have heard tsunami warnings, though.
Predicting earthquakes isn't something that has been perfected yet, so no government agency is going to announce predictions.
Many researchers are working on ways to do this, and have been for decades, but it's still in the research phase. The issue is that earthquakes large enough to provide useful information are not common enough or frequent enough to provide enough data.
Many years ago we had a site that had a remote earthquake sensor. We supported the network connection for it. The data was being fed back to a university in Germany.
I'm currently involved in getting a few connections to remote seismographs for a research project UC Berkeley is doing along the same lines. The connections are all IP based, so nothing you can monitor with a radio.
I do have another site that has a USGS seismograph being fed back via a phone line. Having had to repair the line a few times, I can tell you that it's just a steady audio tone that supposedly changes pitch when the sensor vibrates. Luckily/unfortunately I've never been clipped on the line when there was an earthquake…
So, earthquake predictions are not an exact science, yet. But it's being worked on.
Best thing you can do is be prepared at all times, and hang on when it does happen.
