In Anthem, what significant tests do Equality and Liberty encounter in the forest and how is their journey symbolic?
The journey that Equality and Liberty make through the Uncharted Forest is full of tests, both physical and psychological in nature. Physically, they must survive. Equality 7-2521 seems to have figured out that the talk of all the monsters and beasts in the forest is nonsense, but they still have to eat in order to survive. As such, they make bows and arrows, saying "We can kill more birds than we need for our food; we find water and fruit in the forest."
They also must continue to travel away from the City in order to survive. They aren't worried about being caught, because they know that anyone venturing out to the forest would be left for dead and forgotten, but they need to find more permanent shelter, which they do in the form of the windowed house on the summit of the mountain. At the start of their journey, Equality 7-2521 states that,
We have walked for many days. The forest has no end, and we seek no end. But each day added to the chain of days between us and the City is like an added blessing.
When they finally arrive at the house, you might say that they could be compared to Adam and Eve. They are present in a new, utopic world which they have complete control over. They must populate it with their children and they get to decide upon everything. This is very similar to The Garden of Eden.