We were in Odense last July, 2023. There was no need to pre-book the museum when we were there - you can monitor on the website.
That said, we didn't actually visit the HC Museum. I'm sure you've done your research, but if it is based on one of rhapsodic travel articles or guides, you might want to take a look at some of the reviews from travelers such as on Tripadvisor. Many find the reality didn't match up to the promotion. I get migraines and was afraid of the possibility with the visual displays, but I have become convinced that I didn't miss out.
Here is a link to a discussion of Odense and the HC Andersen Museum on this forum. It includes my ideas on other sites in Odense we really enjoyed and a couple poster reviews of the museum are included. There are differing opinions on and experiences at the museum! https://community.ricksteves.com/travel-forum/denmark/hans-christian-anderson-museum-in-odense-denmark
I never saw info on this museum until we were in Odense. We spent about 90 minutes and I wish we had had a longer time: Odense City Museum Møntergaarden. https://www.visitodense.com/tourist/plan-your-trip/odense-city-museum-montergaarden-gdk631949
I can't help with the ferry.