If one shard was barely enough to repower a single cybertronian in stasis or animated a few appliances, the handful of shards left would probably have been insufficient to repower cybertron to any meaningful degree. And after DOTM, it would be even less likely I'd say, given there really wasnt really... anything... left of cybertron after that, and since all known shards were already consumed.
There's probably a matter of scale here. The Allspark was destroyed while it was small, so the shards are small and perhaps contain less power, unless the power is concentrated. Also a lot of energy was lost when it took out Megatron. When the Cube was on Cybertron it was in its big size and maybe contained more power. Or rather wouldn't have been so badly affected blowing out Megatron while in its bigger state. I'm assuming the Allspark doesn't so much contain the power as it's a conduit for gathering power, such as from the Star Harvester. The fact it had to be recharged at all suggests its power isn't infinite. So maybe if a shard could be powered up enough to restore itself and become big again it might be okay for restoring Cybertron. Pity the Allspark wasn't destroyed when it was in the bigger mode. More shards and perhaps bigger shards too. But who knows with the Allspark? Shit be made up as it goes along.
Not necessarily. Remember, they don't say that energy stays the same, only that it isn't created or destroyed. It could either have been "lost" by transforming much of the energy into a non-usable form (sort of a mystical form of entropy), or it could simply be locked within the Matrix now, which has differnt ways of channeling it and might not be able to be used the same way. The other problem is, as I said, cybertron may simply be beyond even the cube's power to save now.
From a story standpoint it would be senseless to kill off Cybertron completely. Unless we're introduced to a new planet which The Autobots may find refuge, but that's just obnoxious in my opinion. When I saw Cybertron being destroyed it was a bit silly to experience. I'm sure I'm not alone when I say Cybertron needs to be placed back in the story some how.
Technically the first cube did that... seeing as everything it touched it made evil due to its power + it only healed evil robots.
According to Bob Orci interview those were feral Transformers. The Allspark is like the mutagen in TMNT II. Tokka and Razar were animals thus they mutated their corresponding intelligence was that of babies. The Turtles had years to develop their minds. Also Cybertronians don't rely on the Allspark to reproduce. As seen in Revenge of the Fallen Hatchlings are the beginning of the Cybertronian life cycle. And apparently they can have descendants as seen with the Dynasty of Primes and Jetfire spouting his lineage.