My Wyandotte was a horrible broody! Flaky. And when she realized everyone else had chicks but her, she went on a kill mission. Fortunately she only got two babies before I realized.
IF it were me, I would push her out for a walk with the chicks and clean the area. Check the eggs for movement. If you have a problem moving her, I've found a towel can work and the chicks will follow. That doesn't sound like a sanitary environment for the babies.
If she is the dominant hen they will respect her and the chicks' space or I am sure pay the price. None of the other chickens dare go near Betty's babies.
To the last question get a little mason jar waterer and put it on a something sturdy on the floor near the nest. like a block of 2x4 or a couple of bricks. Just high enough to keep shavings out but low enough for the chicks.
Betty, the avatar, is a wonderful mother. She's a Langshan/Sussex mix. She sticks to the nest and gets up once a day for a breather. She let's me check on the eggs and doesn't peck or scream. And when they hatch she teaches them everything they need to know. She's also the boss so integration is...
Each hen is different. I have a Cochin who's been broody every morning for at least a month. In the afternoon she goes out and plays with the other chickens and then roosts for the night and then starts all over again the next day. She never gets any more broody and she never gets any less...