Yes, there are free buses for pickup and dropoff.
Hire a local taxi driver and you can get picked up or dropped off, some drivers do runs to and from Changbai Mountain for around 80 per person if you split the fare.
Yes, there’s a free shuttle bus.
Finding a local taxi driver can have you booked and transferred, some drivers even make runs to Changbai Mountain returning every day for around 80 yuan per person sharing the ride.