That would be true if every economic good were produced within the community. I don’t know how isolated these experimental communities are, but I doubt they source 100% of supplies from the same group that’s getting the basic income.
It's true if ANY economic good is produced locally. You can look for individual prices changes.
Additionally, production costs are highly variable component of local prices and can be dwarfed by transport and retail costs (e.g. produce in the US.)
2) 6000 is a pretty good sample size. Given that this will be universal within these communities, we can certainly look for any evidence of local price changes.