In my opinion, if you're interested in these things, it's really best to do some reading on your own and come to your own conclusions, rather than simply taking the typical responses to these questions as fact. These are common talking points, with common responses, but if you don't come to the conclusions for yourself, you'll just be echoing the thoughts of others without understanding much of the reasoning behind it.

Edit: Briefly, from my perspective: The Non-Aggression Principle suggests that it is wrong to initiate force against somebody else. This is logically derived from the principle of self-ownership, meaning that you own only your own body, and that which you create. Initiating force against somebody else is a violation of these principles, and as such, the party being subject to aggression has the right to defend themselves proportionally.

Roads: I always thought this was dumb, but it is a very common objection to anarchism by people who are uneducated in the subject. Start talking to 'unenlightened' people about anarchy, and this is one of the first things they will probably say. Anarcho-capitalism advocates for truly free markets, and as such, it's reasonable to assume that it would be economically beneficial for somebody to build a road from point A to point B and then charge people a fee to use it. People are often confused and discouraged by this because on the surface, people assume that fees = bad. However, consider that EVERY american is currently paying a 'fee' for the roads in several different ways: federal taxes, state taxes, and municipal taxes. This means that many people who do not drive are paying for roads, and it also means that many people who drive more than average are still paying the same amount as everybody else, even though they are utilizing the roads much more than other people. It makes more sense to charge for actual use, rather than a flat fee to every american citizen.

Somalia: I don't know enough about Somalia to elaborate here, so I'll save this for somebody else more informed.

ancap vs. anarcism: I don't have a good reply for this, but in my own personal perspective, this seems to be a matter of semantics and how you define the word anarchy. To me, anarchy means absence of the state, where the individual is free to do as they please without coercion. I feel that capitalism is natural and inevitable, and I have no problems with it as long as all parties are exchanging voluntarily. A 'true anarchist' would likely say that capitalism's hierarchical nature is inherently predatory and allows the business owners to take advantage of their employees, turning them into wage slaves. But personally, I feel that people should be free to do as they chose, and if this means working for somebody else and getting paid a mere fraction of the value they create, then so be it. I am a Voluntaryist, however, so not everybody here will have the same perspective.

Feel free to correct me on anything I've stated; I'm still developing my views and am very open to be convinced that I'm wrong on these topics. I'm also trying to get better at expressing my viewpoints succinctly (particurlary political ones) and am open to criticism if others feel I haven't explained something accurately.