No, but the park nearby's got food
No, though you gave in and out privileges and there is food nearby.
No, the Otium is the only place inside the museum. However there are several small cafes and restaurants just outside the museum if you walk out the exit and across the green space. As long as you have your electronic ticket or paper copy, you can re-enter the museum, after your meal or snack. Just present your ticket to the museum personnel.
Nope? There's alot of restaurants outside though
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