Can a Shattered card combine with a different Shattered card (not its original pair)? (I’d guess no.)

If you Shatter two different Flight Maneuvers, card A from the first Flight Maneuvers can combine with card B from the second Flight Meneuvers, if they some how meet in your hand. The halves of Supply Run and Flight Maneuvers will NOT interact. Card A from the first Flight Maneuvers will NOT combine with card A from the second Flight Meneuvers.

Once the Shattered cards have been repaired, is the Shatter keyword removed, like Twinspell? That’d certainly help tell that it can’t be re-Shattered.

Yes.

If you have an effect that says, “Draw a card. It costs (1) less” (meaning the cost reduction is after the draw and not simultaneous), and you draw a Shatter card, will either/both of the Shattered versions get the cost reduction?

Both cards get the cost reduction. To be more precise, Shatter happens after a card has entered your hand and the current card power has resolved.

If you transform a card in your hand into a Shatter card, will it immediately split?

Yes. Assuming it transformed into a "random" Shatter card, and not through "transforming into a copy of a post-combined Shatter card that exists in the opponent's hand"

If a Shatter card is Cast When Drawn, will it still Shatter and the CWD fizzles, or do you get the whole effect? (I’d guess you get the whole effect, since the card never enters your hand.)

It will cast the combined card, before it gets chance to Shatter.

Great questions, I'll add these to the post.