The question is up there
In White forest there is the White Treehollow where you can actually battle a lot of trainers until you beat them all.The White Treehollow is also known as Unova Challenge.It is a pretty challenging place.It has 10 floors.Each Floor with its own difficulty.Every level has a boss that you must beat to continue to the other floors.The 10th Floor boss is Alders Grandson Benga.The player cannot enter the Treehollow if he/her has not defeated Alder in Flocessy town.When you beat him, go to Alders place in Flocessy town and talk to Benga.He will give you a Shiny Dratini as a Reward for beating the Unova Challenge Also in White Forest there Shops that sell Evolution stones.They open according to the Treehollow Floor you are.There are people with their Pokemon that you can talk to.You can heal your Pokemon at the Pokemon Center.
In White forest there is the White Treehollow where you can actually battle a lot of trainers until you beat them all.The White Treehollow is also known as Unova Challenge.It is a pretty challenging place.It has 10 floors.Each Floor with its own difficulty.Every level has a boss that you must beat to continue to the other floors.The 10th Floor boss is Alders Grandson Benga.The player cannot enter the Treehollow if he/her has not defeated Alder in Flocessy town.When you beat him, go to Alders place in Flocessy town and talk to Benga.He will give you a Shiny Dratini as a Reward for beating the Unova Challenge
Also in White Forest there Shops that sell Evolution stones.They open according to the Treehollow Floor you are.There are people with their Pokemon that you can talk to.You can heal your Pokemon at the Pokemon Center.
This Guy you say will leave when you beat Alder in Flocessy town.
These are pretty much all the things you can do in White forest