After I take leave to PCS to new duty station, am I expected to find my own way there?

Yes, you are responsible for arriving at your new duty station. You need to report before midnight, the day your leave ends. If you are planning on driving, make sure you have a good plan. If you plan to fly, ensure you choose the nearest airport. Reach out to your sponsor, they will have recommendations for you. Good luck in your future endeavors.

The Army will pay for your ticket from Korea to your new duty station. The leave you take between when you fly away and when you arrive is yours to do as you like.
I'm not entirely certain I understand what you're asking.

No, you will have an sponsor who will guide you through the process and the gaining unit has systems in place to make your pcs much easier. You are not expected to know everything, just be flexible during the first two weeks in.