You won't be able to kill all zombies. Remember that you are just a single human(well, mostly).
Afcourse, but it's easy to just walk pass the zombies. There is a stamina bar in the game, but I think it's just place holder right? It only depletes when you 'walk' instead of 'run', but it doesn't do much. Would love to see that you can't run constantly.
This would also be a great opportunity for 'skills'. I know this can be a pain in the ass to code, but it would be very fun and great to have a system like that in the game aswell. Think about a pistol skill, how more you use a certain weapon, how more accurate she become. How more she 'swims' in the pond, or how much she runs, how fitter she become and how more stamina she will get.
I would also love to see a food/drink mechanic in the game. For example, you can find a lot of fast food, but it will make her less athletic and increase 'body mass' so she will become slower, but her health can increase. And it gives you a lot of energy. Or you can grow/find healty food, which is more 'rare' but it keeps her body more fit, which she can become faster and more stamina.
So, you don't only have the story line, she also become stronger and know how to handle guns, and she has to maintain herself. If you don't drink enough food or water, she can black out and other people need to bring their own life in danger to rescue you.
I don't want to see a survival game that 'punish' you to much, but it would be great if we have some mechanics in the game which makes it feel more like a surival game.