I work as a CNA on an Adult Med/Surg Floor. It is a very hands on job, and can be very physically demanding and fast paced. I previously worked at a desk, and I much prefer being on my feet, interacting with people, and being busy for the whole 12 hour day. However, it isn't for everyone.
Regarding hours, it is pretty easy to work what you need to and still go to school. I work PRN, which means I signed a contract saying that I will work a minimum of 2 shifts in a 6 week period, and I can work a maximum of 12 shifts in a 6 week period. 24 hours in 6 weeks in pretty easy to commit to, but each hospital will differ regarding what they consider PRN. Hospitals usually have a fair amount of PRN CNA jobs since many CNAs are working in that capacity while they work toward a nursing degree or a degree in another medical field. It's a good way to get your foot in the door with the hospital of your choice. Keep in mind that if you are working PRN, you will most likely not receive any benefits or PTO. It's a trade off for the flexibility you get.
At my hospital, CNAs can become certified in additional skills called +4s. These can differ from hospital to hospital depending on your state's scope of practice and your hospital's rules. My duties as a CNA include: taking vitals, taking blood sugars, inserting and removing catheters, removing IVs, prepping IV fluids, basic oral suctioning on awake/alert patients, setting up and beginning/changing/discontinuing oxygen therapy per the nurse's orders, setting up and removing meal trays and documenting intake, basic bandage changes on very simple wounds, assisting with baths, assisting with toileting, turning the patient if needed, ambulating the patient if needed, changing sheets, feeding patients if necessary, escorting discharged patients out of the hospital, sitting with patients who need constant observation, and more. The biggest job of the CNA is to be the nurse's extra eyes and ears - if something has changed with the patient, we are usually the first ones to know because of how much hands on work we do with them, and it is our job to report that to the nurse. The nurses I work with know I am in nursing school and are wonderful about showing me interesting things or things that I should know/will see in school when they have time.
Many hospitals do have tuition reimbursement programs, but I highly doubt they would pay for initial licensure obtained before signing on with them. If they have tuition reimbursement, they will also likely have a cap on how much you get depending on your hours worked, time with the hospital, grades maintained, etc. But, every little bit helps.
Unfortunately, I have never seen a hospital that hires people under the legal age of 18 in a patient care capacity. You could, however, volunteer in some other way - my current manager started as a candy striper at 16 and worked all the way up to the manager of our very busy floor. As for LTC facilities or Nursing Homes, they would have different rules and legal restrictions, so you may be able to find work there at 16. Keep in mind that hospital nursing and LTC nursing can be very different.
Are you wanting to pursue a college degree in Nursing? Starting out as a CNA is a great way to see if it is for you. Keep in mind being a CNA is different from being a nurse in many ways, but it is a great way to hone your basic patient care skills and learn how to build a rapport with patients.