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1) is the root partition the flash memory (ie not on hd[a|b]) ?


The root partition is on disk. /dev/hda5, to be exact.

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If this was full, could it be the cause of sync issues etc?


Unlikely. As Bitt says, it's mounted read-only during synchronisation.

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I installed all of my extrnsions in the /usr folder


IIRC, you can use /dev/hda2, which is 32M, for extra stuff. Mount it under /opt, or something. Alternatively, if you've got two disks, you can use /dev/hd[b|c]5 (the root partition on the second disk).

Also, if you're tight for space, you can keep your shell utils and scripts in /drive0, and symlink them into the filesystem. It's only the things that run alongside the player (and hence might interfere with synchronisation) that shouldn't be on the music partitions.
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-- roger