Your response indicates you've never actually engaged with any anarchist philosophers or thought before, let me ask you this, do you really think no anarchist philosopher EVER thought of any of those points? Research the beliefs of bakunin, kropotkin, and the likes before giving strong opinions on anarchism, else you look unbelievably ignorant to anyone who actually is familiar with the material.
Central authority and law is meant to kept that chaos in check.
Law, sure, central authority? It does the opposite, it causes a great deal of misery and chaos. It is unchecked power held by few who won't give it up under any circumstances, it maximizes the chaos of humanity. Freedom and democracy are the only counter-balance, and anarchists just want to maximize democracy.
Given your example, what would happen if two groups in the same town both elected their own police force with wildly different directives?
Both groups would show up to the meeting and either reach consensus or leave it to a democratic vote. I want to point out that this has NEVER happened in any anarchist society, why do you think this is a likely scenario? If they were absolutely deadset, I suppose there could be a schism, but there's no historical reference for this, because why would this ever happen?
Please, if you're going to try a gotcha argument like this, engage with the material and look for a historic reference. This WHAT IF THIS HAPPENS? can be done with any ideology, if there's no historic reference for it, then sure, it could cause a disaster, but it hasn't ever so why should I care? I can come up with countless theoretical disasters, and real ones for capitalism.
What happens when you give those cops the means to enforce their directives and they decide to enact their own rules?
They'll do poorly at the next town meeting and probably be demoted/swapped out...
How would you even get them to do their job without a centrally backed currency?
They can choose not to do it, of course. There's an idea of mutual aid, I scratch your back, you scratch mine, the people would be grateful for them doing a good job and would help them elsewise, as just one example. Mutualism actually has various currency-related anarchist strategies, a central authority is not needed for making a currency valid, I don't know why you believe that premise to be the case.