I'm a little curious about this, and maybe someone with a better understanding of the data files (or manual) knows:

When the game generates a shard during the campaign, how does it determine the opponents?

Obviously, you only face "Local Lord" opponents before meeting any other Masters, but after that point, you still face "Local Lord" opponents from time to time, and if it's a single opponent shard, it can still be a "Local Lord". However, I'm not sure whether multi-opponent shards can have two (or more) "Local Lord" opponents once you've met other Masters.

Likewise, is there some weighting given to the Masters as potential opponents or is it there an equal chance for each (once you've met them, of course)?

Well it seems like it is rather random.
I once had to go back to the astral because the barbarian stomped me - i did another shard and then went back to the one i had tried before but instead of the barbarian i now faced Oinor even so i didn't defeated the Barbarians home shard yet.

From doing save rollbacks (a backed-up save in the astral, enter a shard and look at what's there, then exit and reset the save back to the astral), it looks like the shard's geography is set, but there's some form of randomization of province populations and sites, along with your opponents, when you actually enter it.

Curiously, the same set of populations/sites often comes up several times before changing, but the opposition seems to change each time (or at least be able to).

Apparently this is how it works. I actually started one campaign, copied the save file and played through the tutorial twice and finished on substantially different turns. The shards are identical.

Try making a save in the astral before entering a normal shard (rather than the tutorial, which has already been generated once you're in it), then exit and restore the save. Do this several times. It seems to stay the same MOST of the time, but then occasionally the population and site configuration changes (and the enemies spawned do too - it's easiest to see this if there are several masters of varying "difficulty" available since Skilled-Skilled-Beginner means you've got a different set than Skilled-Competent-Beginner).
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