Move Time Machine backup from local disk to Airport Extreme disk and share with others
I have run TM backups both locally and across the network.  

Moving backups: 

Just moving the disk won't work.  If you don't need to use the old backups, it's probably worth just biting the bullet and waiting for it to complete a new backup (if you connect an ethernet cable on a gigabit network it's faster (~90MB/s) than connecting the drive via USB (~30MB/s)).  

If you need to keep the old backups, you could try creating a sparsebundle with disk utility, mounting it, and then copying the backup files directly onto it.  This method would be slower than creating a new backup from scratch over gigabit though, so if you don't need the old backups, it doesn't buy you anything.

Multiple machines:  

Yes, you can backup multiple machines to the same Time Machine disk