He and the father and son survivors find a safe harbor in the police station - it has water, food?, communications equipment, weapons, ammo, other vital equipment and they all just abandon it? And split up? Those were the only people he knows are still around and he can trust them apparently, and they all split up?
Rick went to Atlanta to search for his wife and child. The father seemed attached to being close to his zombie wife.
He drives off in his cop car and runs out of gas (didn't he think to top it off? or to carry extra gas)?
I guess not
He gets to the farm where he finds the old pickup truck - I assume he's going to siphon off some gas, but instead goes off on a horse? He abandons his patrol car? It's a safe place with mobility and communications and weapons and he just takes off an a horse?
Horses don't run out of gas and provide companionship.
How does he escape the zombies by crawling into the tank? I'm not an expert, but do tanks have hatches underneath? It seems like the place tanks have most armor is underneath to protect them from IEDs, mines, etc. Wouldn't a hatch underneath defeat that?
Some tanks have escape hatches located underneath them.
I can't think of a great explanation for the hospital stuff. Not trying to be fresh, just trying to provide another point of view