The pop up window issue may well be a third-party app doing this. I have never seen Chrome exhibit such behavior on its own. Still, you might scan through the Chrome browser settings to see in there might be a related option that needs disabling.
The signal strength indicator (bars graph) may not immediately indicate the actual signal strength. I’m not sure what the precise update time is. That said, the problem may also be a cellular node capacity issue. If that tower’s capacity is being heavily used, it might cause a delay in servicing your place in queue. In other words, towers don’t always respond the way we expect them to. If this is a persistent problem seen throughout your usage area, that would surely indicate an issue with the phone or network.