No, it does not. Both of these statements are false.
You're going to need to elaborate a little more than this.
Wrong. Even the victor of a war has massive costs.
Which they then take out of the loser in the form of reparations or territorial gains, which has been standard practice among nation-states for longer than the nation-state has existed.
Individuals aren't capable of the level of warfare that nation-states perform because citizens pay for these costs when nation-states make war.
Individuals group up and pay for wars. You've yet to suggest a means of making this not happen, and you seem to have suggested that it just doesn't happen, above.
The number of people who don't want to pay for war in the US is evidence of this.
The number of people who do want to pay for war in the US (about half he population) is counter-evidence to this.
Again, this is a cost-benefit analysis. It's not as simple as being the biggest. Is the US doing well in the Middle East? We're spending trillions of dollars and haven't "won" so....
So, we aren't as good at some kinds of violence. I fail to see the relevance of this. I'm not arguing that bigger = better. I'm arguing that better = better. Whoever is better at violence gets what they want.
No, this is false. Anarchism does not rely upon sheer non-violence.
So how, exactly, would it do this without resorting to organized force? And how would this not lead to an escalation of violence: why would you having a few defenders prevent someone from coming along and knifing you all in your sleep, or showing up with a LOT of attackers? How are you going to prevent charismatic or wealthy people from acquiring the power they need to topple your anarchist defenders?
There is sufficient evidence to say that an anarchist society could defend itself sufficiently that the benefit of conquering it wouldn't be worth the cost.
And now we're back to the biological underpinnings of violence. Massive, group based violence (read: genocide or ethnic cleansing) is a fairly normal (if uncommon) part of the human experience. It's happened for at least all of written history, in both states and stateless societies. Check out Why Not Kill Them All? for a more thorough look at the biology and psychology of violence.
Because "cost-benefit analysis" isn't the whole story of violence. We resort to violence because it gets us stuff, but that stuff doesn't have to be resources. It can be vengeance, empowerment, pre-emptive violence to prove how badass you are, purification of the filthy "other", all sorts of things.
You can't make violence so expensive it isn't worth the cost. Evidence: nuclear weapons have actually been used. Chemical weapons are still being used. Kurds were gassed with mustard gas not long ago, and it's only been a couple years since Syrians were gassed with sarin without regard for fighting status.
Perhaps you could make a certain kind of violence so expensive that that particular form of violence isn't worth it (as in trench warfare in WWI). But that won't stop people from making innovations in other styles and modes of violence and then getting back to the slaughter (blitzkrieg in WWII).