Sorry Woum! I rushed the tutorial so I understand why it is super confusing. By killing zombies you get to unlock more weapons and abilities for your wheels. The red cross that you start with is just a placeholder for the ability wheel, so it won't do anything until you unlock more.
I hope that makes some sense! I am realizing that I made the game a bit difficult, I just got really good at the game while developing, haha. Here's a hint: I hid a shotgun in the level, if you find it you get a shotgun for free!
Let me know if you're still having trouble, and thanks for giving it a try!