Greetings Katrina and your friend,
Its possible to survive on just mushrooms from the woods as I spend most my time in the woods to.
There are 3 types of mushrooms and non are poisonous.
Not sure if you use an external map as they show where some apple trees are.
Most villages seem to have some fruit trees.
There are often other fruits such plums and pears along the side of roads.
About encounters - experienced survivors say use a microphone to say 'Hello' first - then less likely to get shot.
I never move with my gun out as some survivors think it looks aggressive so they Kill On Sight.
Just a thought, try to stay away from the spawn points on the coast as lots of desperate people come inland.
I'm usually up in Olsha, some friendly survivors up here - but sometimes lots of shooting as bandits can snipe from the hill.
Anyhow, best of luck, and stay safe.