Any way to have a 'Community World?'

Unfortunately, you cannot. You would have to leave your server running 24/7.

On the plus side, you can at least give your friends building permissions, and block everyone else's. The restrictions save to each player, even if they exit and rejoin. That way, they can join or leave at their own leisure without fear of having no permissions, and you can keep an open public server and not worry about griefers.
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"...and when there was no meat, we ate fowl and when there was no fowl, we ate crawdad and when there was no crawdad to be found, we ate sand. "

No problem, sorry
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"...and when there was no meat, we ate fowl and when there was no fowl, we ate crawdad and when there was no crawdad to be found, we ate sand. "