For a list of federally funded health centers go to:

http://findahealthcenter.hrsa.gov/

You can find many more government and low cost resources for all kinds of health concerns at
http://www.simplyinsurancequotes.com/links.php?id=bghott12bq09
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Here you can get quotes for private insurance:
http://www.simplyinsurancequotes.com/healthcomparison.html?id=xyo0tt24m009
more at:
http://www.getinstantcover.motoclassica.co.uk/AmericanHealthQuotes.html?id=xyo0tt24m009

In truth, health insurance works a little differently in each state.

To answer your specific questions:
1) No, health insurance is not compulsory for everyone. If you're lucky, you are able to join a group policy at work. (If you're really lucky, it's a good policy and the employer pays at least half of it.) Some states have recently made it compulsory, but that's such a recent change that there's no clear cut answer yet for how that's going to work.

2) What happens if someone can't afford it is… they don't get it, usually. Except if your income puts you below the "poverty level", in which case you qualify for Medicaid. (In some states there are programs that typically provide assistance with insuring children, though they are few and far between for covering adults.)

3) Health insurance rarely covers all the bills when you have a procedure done. Most plans cover 50-80% after you meet your deductible. The deductible amounts vary widely (but the trend is that the deductibles are getting higher and higher to keep the premiums down.) If you're really, REALLY lucky, you don't have a deductible (which is only an option on group plans), and you may only have to pay 10% of covered charges. (These plans are few and far between. As in, you might have them if you're in Congress.)

4) Yes, the patient has some say over procedures. However, if the patient opts for an "experimental" procedure, or one that isn't deemed "medically necessary", then health insurance may refuse to cover any charges at all.

In the end, as with most things, the middle class takes the brunt of these costs. This has become such a problem that more than 50% of all bankruptcies are as a result of medical bills (and of those, more than 75% had health insurance.)

** Edited to add:
It's not ALL about the money when a procedure is involved. If it is, the state keeps track of complaints filed on behalf of consumers with "managed care" (ie. any type of network arrangement including Preferred Provider Organizations, Health Maintenance Organizations, and Point of Service organizations — also known as PPO, HMO, and POS) and may very well revoke a company's charter to do business in the state should the company be turning down too many legitimate claims.

However, insurance companies are sticklers for following the "standard" for medical care. This is what makes it difficult to answer your question. Because they should not deny anything that's considered standard for care in the given circumstances (should not and will not being two completely different things, of course.) And there may be several options that would be considered "standard." If the patient wants treatment that isn't yet considered "standard", they would balk. Period.

You BUY it on a month to month basis. If you want low monthly payments, you have to cut the coverage – like take a $10,000 deductible. Or higher. That would cut payments down to maybe $200 a month or less.

The older she is, the less healthy she is, the more it costs.

Your best bet, is to find a local, independent agent, who can help you balance cost with coverage.

2) Your parents must be your dependents (or would have been your dependents except for the gross income test) for you to take a deduction anyway. So, unless you are supporting them: No.

You will probably have a co-pay that is due at the time of service. You will then be billed for the 20% not covered by your health insurance.