Yes, to collect Anatomy Book, Rose Bush and Colorful Mushroom, you just need to start the Quest, if you can't go through the door and collect more items, just collect the above-mentioned for a few days as needed, then do the door missions and collect the rest. Until you complete the mission you will be able to collect items, I'm not sure what it will be like if you have access to the door, can you collect rosebush again etc. I wasn't collecting the rest of the items I was focusing on the rose bush and mushroom.