will the ramp from the run to the house be a problem?
Maybe, maybe not. What does it look like? How steep is it or how high? They may be fine but what sometimes happens when the hen tells them to follow her to the coop at bedtime some chicks gather under the pop door instead of going to the end of the ramp to walk up. They can't jump that high. The hen may give up and take the ones that follow her up the ramp to the coop or, more likely, hop down and prepare to spend the night down there. You need to check at bedtime to make sure they are safe.
Will a small waterer do, or will they still need a chick one if their mother is with them?
What does the small waterer look like? Where is it? I use a pet bowl and fill it with rock so the chicks can "walk on water". That way they don't drown if they fall in. They will poop in it so you need to change it daily.
Should I keep a small feeder with chick starter in the run for the hen and chicks to eat alone? Or will she lead them down to the larger feeder?
She will take them to the larger feeder, whatever it looks like. If they cannot reach up at first she will move feed down where they can get it. Before two weeks they will be flying up to eat out of it themselves without any help from the hen, though she will probably do sentry duty.
I don't always do the same thing, conditions change. But if I put a new feeder out for the chicks the other adults often treat it as something special, even if it contains the same type of feed they have elsewhere. I can have trouble keeping enough feed in it for the chicks because the other chickens wipe it out.
In the coop, I use a feeder like this and just lower it to the ground so the chicks can get to it.
View attachment 1769110
Sometimes I use this creep feeder. I put one of those red chick feeders in it so the chicks can get to it but adults (including the broody) cannot. If my broody is raising them in the coop I use the bucket with holes. If she is raising them in my shelter out in the run(Shelter is only used at night for predator protection) I often use the creep feeder. There are all kinds of options as to what you could do.
View attachment 1769111
If so what would be safe for both young chicks and adult chickens to eat?
A standard way to feed a mixed-age flock is to feed them all the same basic low-calcium feed (Starter, Grower, Flock Raiser, or something else) and offer oyster shell on the side. The ones that need the extra calcium for their egg shells seem to know it, the ones that don't need it do not eat enough to harm themselves.
Basically I’m asking how much of the “taking care of and raising.” Will the mother hen do, and how much will be left to me.
Welcome to raising them with a broody. You will probably really enjoy the experience if you can relax. I understand you don't want to cause harm so your questions are good. And until you get experience it can be hard to relax.
I don't now what your facilities look like. Broody hens have been raising chicks by instinct alone for thousands of years, often with no real help from humans. But this is generally where they are not restricted. The more you restrict them as far as space, food, and water the more you have to do.
Basically what you need to do is have food and water where the chicks can get to them. The broody hen will take them there. You need to provide predator protection. At first you may have to physically move them to a safe place to sleep but soon the hen should take them in herself so all you have to do is lock the door at night, if you need to do that much.
I personally like to leave as much as I can (which is practically everything) to the hen. I figure she knows more about it than I do and the less I interfere the less harm I do. Other people like to try to micromanage everything themselves. I guess they don't trust a broody hen. Depending on your set-up and conditions you may need to do more than I do.