You need a ticket. Its possible to just show up and get tickets the same day. Thats what I did but it was during off season winter. You can kind of tell if they are selling out by looking at their ticket availability for the coming days on the website. Better to get them before hand.
To do the tours and get near the castle you need a ticket.
Yes.
You can enter the visitor center without a ticket. You need a tour ticket to be able to board the tram that takes you up the hill to the castle. It is highly recommended that you get tickets in advance because there are a limited number of spots available for each time slot. Without a ticket reservation, you may be waiting hours before you can board the tram or the entire day may be sold out.
Yes you do need a tickets to get to the Castle.
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