In the opening scene, just after Maggie kills the walker by crushing his skull, as she's moving off the top of him, you can see its chest rising and falling twice.
Based on the age of Herschel, it is at least 14-20 years into the zombie apocalypse. The Marshalls are driving cars, which may seem impossible, as gasoline becomes unusable after a year or so. However, it is later revealed that The Croat and New Babylon are creating their own gasoline.
New Babylon Marshall Gritz is armed with an M4A1 assault rifle (or something similar like an M16), with a standard size magazine. He uses several sustained bursts of fully automatic fire to thin out a herd of walkers. Altogether he fires around 15 seconds worth of full auto fire without reloading. The M4 wasn't designed to be a dedicated machine gun, therefore it has a limited magazine capacity compared, which is why it's a select-fire rifle and usually fired in semi-automatic or burst mode. A standard M16/M4/AR-15 magazine has a 30 round capacity, and the M4A1 has a cyclic fire rate of around 700-900 rounds per minute, which is about 12-16 rounds per second. So a 30 round magazine would be emptied in 2-3 seconds of full auto fire.