Highways:
You argue "toll-road" galore as if it would be a bad thing, I am of the opinion that paying for the roads as you use them is a good thing. Densley populated areas suffer because of this "free road" system - putting a price on things puts a limit on demand, which can be used to control congestion.
I don't know exactly how highways are funded in the US, so I'll just go on the basis of how it works in the UK. In the UK, each year, you pay a road tax, this tax varies depending on the car you drive (age, carbon output, etc, etc). Once you have paid your road tax, you have unlimited use of the roads. I'll now borrow an example form one of my favourite books (The Undercover Economist):
A student bar at the University hosts an event each week, students can either choose to buy a ticket for £2, which entitles them to unlimited soft drinks, or a ticket for £10, which entitles them to unlimited alcohol. What the University finds, however, is that the vast majority of students buy the £10 tickets, and drink an amount that is a) unhealthy, and b) detrimental to their studies. The university tries to curb the drinking, so they decide to double the price of the alcohol tickets, to £20. The result of this is that while a few people do switch down to the non-alcoholic tickets, most carry on with the £20 tickets, and continue drinking the same amount, if not more.
When applied to roads, the Government is the University, the alcoholic drinks are the miles driven, the expensive ticket represents the road tax, and the cheap ticket represents the shitty alternatives (public transport). Much of the UK, particularly South East England suffers from severe congestion. I live in a village, and yet for 2 or 3 hours of the day, the roads can come to a complete standstill. In the towns nearby, you can end up spending a very long time in traffic. One of the ways that the Government has tried tackling this, is by increasing road tax. As you can see from the example, it helps a little bit, but not enough.
The problem with the one-off pay system is that the amount you pay per-mile reduces with each additional mile you drive. In essense, you have every incentive to drive more, as each time you drive, you get better value for money (on road tax, fuel duty is another matter).
So, no, I don't see road tolls being a problem, particularly in the modern era, when the entire system can be automated, with no stopping at booths. The companies also have an incentive to keep the traffic flowing as freely as possible - which means things like road maintenance will be better, along with break down assistance, crime prevention, etc. The road companies will want as many cars driving down the road as possible, each additional driver is more money in the bank. You argue that some roads will hold a monopoly position, and, yes, but that will be the exception, and not the rule. For most journeys, there are multiple routes that the driver can take, or they can get a plane, or a train, or not travel at all - each one of those options is something that the road owner would have every incentive to compete with. If there really is a situation where one company holds the rights to the only route which has really high demand, and they exploit that position... well, then I'm gonna make a jump, here, and say that land is cheap and underdeveloped (else there would be more routes), and the high profits from that company would easily attract a new investor to build an alternate road.
Healthcare:
Yes, the US healthcare system is up the crapper. But it's the furthest thing from a free-market system. The Government mandated tax incentives for health insurance essentially makes it favourable for people to buy the worst kind of model, couple that with all sorts of laws preventing cross-state competition, a broken legal system, and Government intervention removing the bottom of the prices (when the Government provides for the poorest, the market no longer needs to cater for that income bracket, they can charge pretty much what they want), factor in Obama's reforms that will make costs increase even more in the long-run, and take the industry further away from a free market.
By far the best solution to healthcare in the world is the system that Singapore uses, Medical Savings Accounts. Read up on them, if you want (basically, Singapore manages to achieve one of the best healthcare systems in the world, with the lowest infant mortality, and highest life expectance in the world, while only costing 3% of GDP (1% public spending, 2% private). Now, I don't agree with how Singapore enforces the system - as it's essentially forced - but you can buy these accounts in the USA. The problem is, so few do, thanks to all of the Government pandering towards the insurance companies. Again, this is not the kind of Government that I advocate.
Education:
Education is difficult one, for me. As children need an education, but obviously, they are reliant on the parents to provide it. However, I do feel that education should be handled at the lowest level possible (at the very least, removing federal control, and having it handled by the states... if not pushing lower). I would also recommend that these states/districts/cities/whatever implement a voucher system. This would allow for competition, and for private companies to get involved, while also assuring that the children from the poorest families receive a high quality education.
Again, for me, education is hard because those who benefit from it, aren't the ones who pay for it. But that doesn't mean the federal government should get control of it.