score:4
(1) Kosice train station opens at 0345 each day. I found I could get in earlier by entering from the platform side of the station. The ticket office opened at 0600. The train was almost empty and I doubt there would be any problem with over booking based on my experience.
(2) I didn't buy the return ticket at the office. I booked an online ticket from Kiev-Chop at the Ukrainian railways website. I then purchased a ticket at Chop train station to get me across the border back into Slovakia.