I am no expert but I did several broody hatches last year and I will answer based on my experience.
How good a mother just depends on the hen, some are just naturally better than others.
How well she protects them depends on the aggressiveness of the other hens and her place in the pecking order and her personality, but most likely yes.
My nest boxes are as high or higher. I just put a huge pile of shavings on the floor beneath in-case one fell out and once one goes to the ground, usually mom follows and so do the others, then they will nest in a corner somewhere until the little ones are flyable.
I put food and water in the nest for the day after hatch.
I leave the chicks with mom unless she proves she can not protect them. I once had to remove a chick as mom was getting ganged up on and the chick was at sever risk, otherwise, they will be fine togther.
One thing that I do, if the broody is nesting with the flock and the other hens have access to the nest, I mark the eggs I want to hatch and remove any extras each night. at about day 17 or 18, I set up some kind of barricade to keep out the other hens and I put food and water in with mom. That is to protect the eggs as they hatch. I had a very clumsy hen who insisted on laying where the other was brooding and mom was not aggressive enough to keep her out and she accidentally crushed some of the hatchlings. I leave the barrier up until the chicks are ready to go to ground, (you'll know, they run around like crazy) and then remove the barrier and keep a close eye on everyone the first couple of days to see how everyone is getting along.
Good luck!