I'm not sure how I am supposed to get away while being surrounded by enemies that I can't even attack.
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You can attack zombies by dragging your inventory cards (bottom row) over them. The red numbers indicate attack value. You should be prepared for that, so having a crafted weapon before attacking any of them is advised (or at least a good amount of items). Do not attack zombies too early. Once battle started, you will get away only by defeating all of them.
Okay, so you try to attack them right in the beginning? I recommend ignoring them and passing by, taking a swing to the West and explore whats over there. Come back later when you are more prepared to fight both of them. You can also try to lure only one, but even then, doing this in the beginning is is pretty risky and you will loose too many items.
It was not the case. I have missed another hint from Tutorial - in "Gather", for some reason it was not clear for me that I should "click" on the gathered item to actually collect it. It was intuitive that I received the items instead of watching on them and go away. Maybe it is needed to implement an "auto-collect" the items upon reveal.