I'd leave it alone. You don't want to stress her out too much. If the nest hay gets a bit too bloody, I carefully remove what I can and add some fresh.
She will allow them to nurse twice a day, but they will also start to munch on hay and feed and drink water on their own. Hay and feed should be accessible to the kits.
Alfalfa pellets and hay should be free fed to lactating does and kits. BOSS helps boost lactation, so now that they are starting to wean, you can lay off those. Oats are fine. The kits get all their digestive enzymes from their mother at this point. That means, anything she can eat, they can...
My does are experienced at kindling and always deliver their kits in the nest boxes. First time moms may need a bit of supervision to make sure that if a doe delivers a kit out of the box, you are there to get the kit in the box before the kit chills.
By the time they are big enough to leave the nest box, they have enough fur to keep warm. And I've yet to have a kit that wasn't able to figure how to get in and out. Once they are able to get out of the nest box, they begin to eat hay and pellets, so pay special attention to keeping feeders and...
Just about anything will work. Some does prefer shavings, some prefer hay. Both of my girls kick out shavings, so I just give them a pile of hay in the corner of their cage, and they do the rest.
Another trick is that you can use dryer lint if your doe doesn't pull enough. No, if using old fur, it doesn't matter which rabbit it comes from. My buck was shedding during my last kindling and I added some of his fur to the pile the doe had made.