❓ Do you need to rent a car in South Korea?
No. I travelled all around the country in 3 weeks by combining buses, trains and the metro, without ever needing one. Public transport covers almost the whole country, including the national parks.
❓ Do you need to speak Korean to travel in South Korea?
No, conversational English is enough to get by, with the help of a translation app like Papago. A few basic words (hello, thank you) are always appreciated, especially outside Seoul.
❓ Should you go to Jeju Island?
I haven't visited it yet, and I didn't include it in my itinerary. For a first trip, the mainland cities already offer more than enough to do: in my opinion, Jeju isn't a priority.