Domestic Army
Switzerland doesn't have one. Every citizen owns a rifle and is trained to fight. That's a big reason Hitler didn't want to attack it.
Basic Preventative Health Care
Free clinics for those who need them, and hard lessons learned from not taking care of one's health, not knowing some basic health information, and not owning health insurance. Even if you are poor, if it's something as important as your life, I would hope people would be compelled to spend money on health rather than a new TV or video game (they don't, now, because they know if they get sick, they'll just go to the emergency room, and get treated using someone else's money). I'm actually very glad ObamaCare passed for this reason, even if a legal mandate isn't as "educational" as a hard life example.
Infrastructure
Private power (already exists), private water (already exists), private rail (already exists), private roads and bridges (already exist), etc. Infrastructure actually hurts us in some way, by forcing us to stick with old technologies that new things can't compete against. Part of the reason the rail system in US sucks is because it can't compete with subsidized highways.
Education
Private schools (especially if funded with "war" money)
Incarceration Facilities
Many prisons in US are already privately owned
Elections
won't exist or be needed
Archival of Historic Records
private collections by hobbyists (you should see mine), or museums funded by visitors
No I don't think they can be paid for voluntarily because people are in whole pretty selfish and irresponsible. This is why I think AnCap will never succeed unless you can change this aspect of human behavior.
You are projecting your own selfishness on others. Also, people who are selfish and irresponsible will quite literally die off in AnCap society, where you NEED to build relationships and communities to survive. You can't just work 9-5 for a crappy wage, have your money taken to pay for things you yourself should be responsible for, and spend all your time sitting at home playing videogames without giving a crap about anyone else. Well, you could, but at the first bit of trouble you'd be royally screwed.