No, anarcho communism cannot be applied, except for one big communist government owning and controlling everything.

I have to disagree. Not only can it be applied, but I believe it be a more sustainable, efficient and free form of anarchy than capitalism. If you are interested in my reasoning, see my comment here (I don't want to repeat myself).

If you "bought an island" or some other land, you agree that land can be owned as property. Also to earn that money, you need to work and sell your products and services, meaning you agree that your labor has market value.

I don't agree with either proposition, but as with any ideology, you have to start somewhere. Otherwise, the system will use force to oppress your ideas. I don't think any anarchist pays taxes or submits to the force of the state to some degree because they believe it's the ideal thing to do, but because not doing so would simply be foolish and counter-productive given the state of things.