Depends who you talk to really, I'll try to answer, but I'll probably do a shit job of it.
-Would anarchism involve money?
No, In an Anarcho-Communist society will be based on a
gift economyIf your vision of anarchism demands that all vestiges of capitalism anywhere in the world be wiped out, how can that be libertarian?
Well first off, its not demanded that every last trace of capitalism be destroyed, its an inevitability. Once the state collapses, the monopoly on force that is used to uphold the capitalist's property rights will wither away. More and more people (hopefully) will choose to change to a more egalitarian society and any remaining capitalists (most likely bosses) will be without a workforce or club with which to coerce people to follow their corrupt system. Secondly, how is destroying an oppressive system in any way oppressive? We can't force people not to subscribe to that system, but as I wrote above, it likely won't work without a system of government to force people into it.
If there would be no money in anarchism, how would people know how to efficiently manage scarce resources (such as if one kind of steel to be used in building a bridge is more reliable than another kind, but is much harder to find)?
I don't have an answer for that, sorry. Anyone else?
What's the difference between property and possession?
From wikipedia
The individual would be perfectly free to create something and keep it as long as it is not a crucial means of production for the community or general public. So an artist's paintbrushes would not need outside approval to be utilized, and the same basic principle would apply to other personal items such as one's toothbrush, musical instruments or book collection, which others needn't tamper with. However, if the matter at hand involves production for society (such as a factory which makes toothbrushes, musical instruments or books), it would become a social possession, accountable to all who work within it and the consuming public. In that regard, anarcho-communism could be considered a compromise between collective and individual use.[48]
If I run a store out of my home, can I kick out people who try to steal stuff, since my home is a possession?
You won't be running a store in an anarcho-communist society.
-How can you have markets without property, if markets depend on people being able to deny access to things they don't have a personal use for?
Again you're presupposing we use a market system similar to the capitalist one.
-If I spend all my life building a boat, is it okay for someone else to destroy it, since it's just "stuff"?
uhhh...No? what gave you that impression?
How long do you think we can have a free and democratic society if we insist on maintaining totalitarian systems in our companies? We must have freedom for individuals and organizations to grow and to realize their potentials.
(Delmar Landen, Head of Organisational Development at General Motors, 1981)