This is getting off topic, and say what you will about America's atrocious healthcare system, but the fact that it is not fully socialized is NOT the problem. Real problems: artificial non-market based demand created by partial socialization (medicare and medicaid buying programs) raising prices for the non-socialized group, oppressive FDA (costs 1 billion usd on average to push a drug through), oppressive occupational licensing (very high barrier to entry to becoming a doctor), imbalanced IP system (especially for chemical/drug patents), and plenty more. Eliminating these problems would go a long way to making America the world's best healthcare system (it already is in some regards -- do some research on where all the prime ministers of social medicine countries go for their important surgeries since their systems haven't incorporated the American medical tech yet).
There are still issues to consider with emergency care (where there is typically not market-based selection of your healthcare) but I think government incentives aiding a market based system (similar to the incentives created by Singapore, arguably the best current system) would create a system so superior to any other country's medical system, that it wouldn't be such a central political issue.
Universal healthcare itself is a huge discussion but seems off topic here.
This depends on political context. In much of the western world outside the US (and partially in the US) healthcare is a publicly funded service. If you pay for your neighbors healthcare, then your neighbors obesity is an externality.
> or cigarettes, on the other hand, there are two potential externalities to tax.
And again here: my neighbors lung cancer is on my taxes, so effectively the only fair cost of cigarettes includes all treatment from all smoking and of course all lost tax revenues from the sick smokers who couldn't work etc. That's a lot more money needed than to cover just second hand smoke as an externality.
And even if you don't factor in public healthcare, an unhealthy population is an externality although not as immediately obvious.