Hi MiDiem,
For starters, chirping is normal at this age. Most young chickens will chirp a lot if they are separated from it's flock or mother hen. If you plan to keep this chicken, I would suggest getting another one close to the same age, so it is not alone. Chickens are social and need a flock mate. It is not healthy for chickens to be raised alone. Another chicken will provide comfort and security for each other. They will eat together, keep each other warm at night, learn to communicate, etc.
I can't answer what breed it is, but it looks very pretty and appears a young pullet, which the name for a young female chicken, or young hen that is not laying eggs yet. I would guess by it's size and the new feather growth on it's head that it is around 5 or weeks old.
You can put a dish of water and a dish of chicken feed in it's cage. It's important to change and refill the water often. 1 cup of feed in a dish at all times so the chick can eat at will should be more than plenty at this point. You can also put dirt and sand or straw, wood chips, dried grass, leaves or a combination of things found outdoors for them to bed on and poop on. When cleaning out their cage, all the material can go right into your compost pile. You can purchase other items offered as bedding, but I suggest you stay away from pine shavings, as chicks sometimes eat it and cannot digest it. It will remain in their crop and they can die. You can find straw, wood pellets and other items for bedding at your local Feed store, if you go that route.
Many people feed layer crumbles for young chickens until they are anywhere from 8 to 12 weeks old. Once they get bigger, their beaks will be large enough to transition from the layer crumbles to layer pellets. Whole grains choices work well too. You will find a variety of poultry feed at your local Feed Store. In addition, chicks like fresh torn up grass from the yard, sprouted black sun flower seeds, or just the seeds, oatmeal, watermelon, any green leafy veggie, like lettuce or kale, berries, pasta, cooked rice, apples and tomatoes. I am sure there is a long list of things that they would eat, including meat, although I wouldn't recommend giving a young chick meat. Some people feed their chickens scramble eggs, raw eggs and yogurt mixed in raw oatmeal. When free-ranging chickens will eat a variety of grasses and weeds, bugs, worms, dirt for grit to assist with digestion, and I have seen hens running around with a small wild baby bird, mouse, rat and other small outdoor wildlife.
Chickens like digging in dirt. They will lay in it and fluff it up around their feathers to keep the mites and lice down.
At this age, this pullet should be able to endure warm weather temperatures without needing a heat lamp. It you were in a colder climate, I would suggest providing a heat lamp for additional warmth on cold nights. Straw used in the bedding will assist with warmth.
It sounds like you are caring for this youngster pretty well on your own so far. The best thing you can do for this chick is to provide it a soft towel kind of bunched up a bit or a small soft stuffed animal to put in it's cage for it to cuddle with at night until you are able to get another chick as a flock mate for it to grow up with.
I hope other than not knowing what breed it is, that I answering the rest of your questions.
Enjoy your new found family addition. Congrats!
