Boy, oh, boy, Nap . . . what an opportunity you have given me to get my geek on.
In order to answer both questions, you first need to determine the type of zombie you are dealing with. Not including the non-fictional voodoo reanimated, there are basically 2 kinds of zombies (the real voodoo related type not included), the slow moving and the fast moving.
Slow moving zombies aren't too threatening, as they can only slowly saunter toward you, due largely to rigor mortis. If you can run, you're pretty safe. The only exception is if there are LOTS of zombies and you're surrounded on all sides. You may have seen these zombies in such films as Night of the Living Dead and Shaun of the Dead.
Fast moving zombies are a much larger threat. Not only can they run, but their post-mortem abilities generally include super strength. In other words they can run FAST, and often can break through commonly sought refuges, such as wooden doors and car windsheilds. You may have seen these zombies in such films as 28 Days Later and Dawn of the Dead. Even more frightening, there are some classes of super zombies that harbor intelligence, and seem capable of battle tactics similar to the Spartans. They tend to travel in large groups, and like Zulu warriors and velociraptors, surround you on all sides when you least expect it. In these cases, survival is damn near impossible. You may remember these zombies from films such as Planet Terror and Return of the Living Dead.
Enough geekery? On with the questions . . .
<i>Just out of curiosity, how does one become a zombie?</i>
According to George Romero, creator of the "Dead" movie series, and the person responsible for the modern movie zombie, the answer is simple: nobody knows.
Really people, in case nobody told all of us geeks, there are no such things as zombies, so why bother spending time trying to figure it out?
Is that answer not good enough? OK, on with the answers. In the case of slow moving zombies, the most common theory seems to be radiation. Some sort of unseen ion can jolt the brain back into action, albeit only part way, making the dead wander aimlessly and desire to consume human flesh.
In the case of fast moving zombies, the most common cause seems to be a virus, transmitted via bite. It basically numbes the brain and turns the human into a mindless flesh seeking machine.
Fast moving intelligent zombies are usually the result of a military designed chemical experiment gone wrong. One might ASSUME that the U.S. government was trying to design a new and unkillable type of soldier, but, as usual, tampering with nature went terribly wrong, and now there is an unstoppable army of the undead.
Another theory, which I've never understood, is that zombies are God's wrath. In the book of Revelations, when Hell is full, the dead will walk the Earth. I don't understand how this applies to zombies. Generally speaking, there's a way to "re-kill" them, so this doesn't seem very plausible to me.
<i>If a zombie eats your brains do you die, or become a zombie too?</i>
Generally speaking, no.
With about 2 exceptions I can think of, you can kill a zombie by destroying its brain. Therefore, if your brain is eaten, you are not a zombie candidate. Also, with only a few exceptions (the above example from Return of the Living Dead included), zombies not only crave eating the brain, but they want to eat the entire body as well. If you are consumed by a pack of zombies, there is often too little left of yourself to be reanimated.
There are a few exceptions to this rule, but for the most part, no brain, no zombie.
