1. What are bthe ways to increase the productivity of the forest?

Answer 1

The forest is most productive, converts most available energy (sunlight) and raw materials (water, soil) to plants & animals when left to its own devices - which have evolved optimal processes over billions of years.

This is the premis of permaculture.
Then to increase the productivity for specific human benefit, learn from the native forest, study traditional local cultures for the particular forest (ethno-botany) and how they interacted with the forest, small clearings, spreading seeds, encouraging game, sustainable resource usage ...
After a year of observation, using permaculture design principles, you should be able to adapt to find a sustainable approach to ensure long term productivity

Answer 2

Preservation! Leave the forest alone!