It sounds like she is not broody. There are many things that indicate a hen might be broody. I've seen hens display practically all of them for a week or longer without flipping over to full broody mode. I've seen hens immediately go broody, not wait. My test is that if the hen spends two consecutive nights on the nest instead of roosting in her normal spot I'll trust her with eggs.
I'll try to answer your questions anyway for net time.
She is about 7 months old, is she old enough to raise chicks?
I imagine they wouldn’t go broody if they couldn’t.
You can get different opinions on first time broodies or pullets going broody. I've had just as many problems with hens that have successfully hatched and raised chicks before as I have with first time broodies, let alone one that has just gone broody before and never hatched or raised chicks. I've had a lot of success with first time broody hens. If you really want a broody to hatch for you, I'd take my chances when you have a chance. For some people these chances don't come often. You might have great success, you might have full failure whether you try now or whether you wait. That's just the way life is.
I’ve read different posts saying they need to be separated from the others. What is the best way to go about that?
Some of us separate broody hens from the others while incubating, hatching, or even raising them. I don't. Instead I mark the eggs I want her to hatch and start them all at the same time. You can collect them while you are checking to see if she is to be trusted, easily up to a week. Then I check under her each day after the others have laid and remove any that don't belong.
Once I have her in her own area away from the others, what do I need to give her?
Do I give her different feed?(she’s on all flock right now)
Do I need to add anything to her water?
What bedding/nesting material should I use?
A feed low in calcium is great, as she is not laying eggs. As others said, All-Flock works really well, now and after the chicks hatch. She and the chicks can eat Starter, Grower, All-Flock or something similar after the eggs hatch. I personally would not add anything to the water but some people add things to the entire flock's daily water. If it is safe for the flock it should be safe for the broody and chicks. What nesting material are you using now, whatever it is should work.
If I keep her in any kind of crate, do I let her out? If so, when and how often?
I'd make the pen or crate big enough for food, water, a nest and a little room to go poop. She should know by instinct to not go poop in the nest but that instinct does not stop her from pooping in water or food. Make it fairly easy for you to clean out.
I would make that pen so she could never leave and no other hen can get to her nest. I would never let her out. Some people may let them out but the purpose of isolating her is so she has no option but to return to that nest and no other chicken has access to her nest. Why isolate her to start with if you don't really isolate her?
One warning if you isolate her. Make sure no chicks can escape that pen and get where the broody cannot protect them or take care of them. The chicks can be in serious danger if they get away from the broody hen's protection and care.