The fiction section was converted into children's books / a children's books section / a children's books You use 'which' appropriately. You can't replace it with 'that' without changing the meaning. It depends on what you want to emphasize. If you want to emphasize what happened to the fiction section and what it was replaced with, keep the sectence as it is. If they already know that there is a children's section and it is next to the children's area, but you want to tell them what happened to the fiction section, then you could say: The fiction section was converted into THE children's book section THAT IS adjacent to THE new children's area.

I think ‘replaced with’ is better than ‘converted into the’ because all that probably happened is that the books on the shelves were changed, there was no building work. I would delete which and simply use and.