For future reference, Government Center to North Station is only around a ten minute walk.

Regarding basically everything MBTA related downtown, it's all very walkable. So unless you aren't comfortable walking, absolutely do that if there's issues with the MBTA and you can't miss a train, because once one of them is late you'll miss the rest of your commute 99% of the time. Pull up Google Maps on your phone and set it to your destination and your current location, it points you which direction to walk in and you'll see if you're going down the wrong street in real time.

As to your question of what was happening with the green line, someone tried killing themselves at Park Street a few hours ago. Half the red line was shut down. So could be that.