The people at the Welt are very accommodating. Due to various family and work schedule issues, I had to fly in and pick up the car by myself on a Friday. My family arrived Saturday morning, and we all went back to the Welt and visited the museum. They gave us passes to park in the garage. Sunday we drove to Neuschwanstein; our factory tour was scheduled for Monday. They gave us parking passes for the garage for the factory tour too. Also, they had no problem with us using the premium lounge on all three days that we were there, food included. Basically they treated us like we were the best customer they ever had!
To answer the OP’s first question, a couple of hours is probably enough for the museum, and the factory tour is about two hours also. If the delivery schedule works out you could do all three in a day, but best to plan for a day and a half. Ask them for parking passes, and the lockers in the lounge are handy for the plant tour as you can’t carry anything in with you.
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