If you're interested in a dice system(which covers combat and non-combat scenarios, as well as loot from both bodies and buildings) I am your man.  

I ran a Walking Dead inspired RP a while back, and the system I cobbled together worked brilliantly, but interest simply petered out and people disappeared.  

As far as cure, scratches, etc: In my RP, what we did was just have a bite have a [i]chance[/i] to infect.  We'd roll a die to determine if the character survived the fever.  I thought that was a lot more reasonable, personally.  

We also had stats for weapon classes, so everyone was allowed to start off either familiar with a particular one, or else be equally ignorant of most weapons(depending on the player's point allocation).  Because tons of people in America [i]do[/i] know how to shoot despite not working in a field that requires it.  I do, and I'm a freaking cosmetology student.  It really does depend on what part of the country you're in, but almost everywhere has people who can shoot.  And as a matter of fact, people who can shoot and who own guns are the most reasonable people to have survived the first waves of a zombie outbreak that shut down most of civilization.  

As far as the reason for military breakdown(which is a really big barrier to suspension of disbelief in this kind of world), it could simply be that normal civilians started to lose faith, looted, were shot, shot back etc.  It doesn't make sense for a zombie outbreak to take out a military, but it [i]is[/i] a necessary assumption for this type of RP to exist.