Ceder perches are fine(cedar shavings aren't safe). The dark brown on her beak is just coloration, you can tell if they're ready to breed by their cere
Not ready to breed
Cere turns white when very ill
I'd avoid lettuce, it has close to no nutritional value. Dark leafy greens like kale, broccoli, spinach, dandelion leaves, mustard greens, and collard greens are extremely good for them and also have a lot of calcium. Carrots are good but have a lot of calcium blockers in them. Like carrots other orange foods are great for birds. You can give them pumpkin, sweet potato, squashes like butternut or acorn. Birds also like grains, cooked quinoa is full of nutrients and because of it's small size is usually accepted by small birds. And boiled eggs are great :) You can also microwave the shell for 30 seconds(to destroy any bacteria) and give it to them too.
If you have some of the foods above available to you definitely include it in their diet, some foods can even be frozen and defrosted in small amounts when needed. It's better to get their vitamins through foods rather then water additives as they can get too much and become ill. Also make sure they have two water dishes whenever using vitamins, one with the vitamins and one without.
Almost forgot, make sure they get at least 3 hours of sunlight(with shade to avoid overheating) a day, you can also use a UVB light instead but it has to be on at least 8 hours a day. They need sunlight to process their vitamin D.