1) Most employer provided health insurance is deducted "pre-tax" so there is no deduction on the tax return.

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.

most insurance will cover the costs you mention if the doctor thinks it is medically necessary.

You've asked a very broad question. There is no simple answer.

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.

Well, if she's 40 and perfectly healthy, it's going to cost her about $500 a month to have a low/no deductible plan that covers checkups.

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.

When you get health insurance, there is what is called a premium. This is the amount you pay on a scheduled basis. For instance, if you get insurance through your employer, you would pay your part of the premium each payday.

If you pay your premiums on time, you get to keep your insurance. Now, when you use your insurance, there is what is called a deductible. This is an amount of money you must spend before the insurance starts paying anything. A typical deductible might be $250/year for the policy holder and $500/year for the family. So, if your dad had the policy and went to get a prescription, if it was his first prescription of the year and it cost $100, he would pay $100. Every time he used stuff under the plan, he would pay everything until he hit the $250 deductible, then the insurance would kick in. (the same goes for the family coverage, until the $500 was met by everybody in total – not separately – you would pay 100%).

Now, once the deductible is met, the insurance starts picking up some of the costs…usually the costs are based on what doctor or provider you use. If you use someone who is called "in network" the insurance company pays more of the bill. They do this because they have negotiated lower costs with that provider. For example, let's say you need to have some tests done and your family has met all your deductibles. Let's also say the tests normally cost $200. If you go to an in network provider, the insurance would cover 80%. If you go out of network, the insurance might only cover 70%. Now the nice thing is, by going in network, you get the discounted price, let's say $160. So, if you go in network, you would pay $32 for the tests and the insurance would pay $128 (totaling $160). If you went out of network, you would pay the 30% of $200 or $60 and the insurance company would pay $140. So, by staying in-network, both you and your insurance company save money.

Also, there is something called an out-of-pocket maximum. This just means that if someone in your family gets real sick or injured, the most you can pay for that year is the out-of-pocket max…say $5,000. Once you hit that, everything after that is covered 100% by your insurance and you don't pay anything.

Last, there is a co-pay – what this means is that if you go to the doctor for a routine visit, it is usually covered without worrying about the deductible and you pay just the co-pay. usually this is $15 or $20 on say a $100 office visit and the insurance company pays the rest (based on a negotiated amount).

And that's the short version of how insurance works.

You can use this site.
http://top-usa-health-insurance-comparator.blogspot.com/
to compare various health insurance providers at your place.