Cost questions: mostly for balance. As for why some elements are a LOT better upped as a result (Gravity), perhaps it's simply because they're not very good unupped.
Momentum is meant to be counterable by Lobotomizer.
More than 6 copies/smaller decks: combos (OTK's, quanta denial, Fractal and buff decks, etc.) and rushes would become a lot stronger. They're already very strong.
SoR Deja Vu was able to perform 2-turn wins when SoR wasn't nerfed.
Yes, Fire Spirit could use a buff. Is cost reduction better than HP increase? Probably not.
Disquake wins more often if the combo gets out. It gets out in a small majority of games. Besides that, CC is the killer.
Immo vs Grabbow: same here; CC is the killer. Immo usually needs to draw PC for Fog too, which is a small advantage for Grabbow. Grabbow is more stable, likely wins a bit more.
Blue Nymph is very strong but not that hard to counter. Not OP. Quantum Pillar+Nova might be OP. QP on its own doesn't seem OP.
Nymphs for 1 million; not much impact at all since most will never afford that. Furthermore, Nymphs do not have a large impact. Some top tier PvP'ers would eventually use it to their advantage and possibly some match at some point in time would be decided by this. Maybe.
FG PvP was done in a PvP Event. I'd look that up for an example of how it went.
15 chosen top cards: again, rushes and combos would dominate pretty hard, especially now that we have SoFree (makes rushes less fragile). Combo decks especially would be brutal, as you could get perfect hands with the likes of Devtal, etc.
Gaining from ups: yes, rushes and combo decks (many are not possible until ups).
Imo, a card space is worth a lot more than 1 quanta, but it depends on the deck you run. In a Cremation rush you don't mind cards disappearing to gain speed much, for instance, but in a fat stall every card could be the difference between a win and a loss (for instance Improved Miracle).
Shards were considered too neutral without something that ties them to their Element, so zanz decided to give each Element an incentive to use its own Shard.
Building a rush: the most important thing is to balance your quanta. Using QI is only the start; you have to test it. Secondly you have to make sure you don't have too few creatures (high-cost creatures will create this scenario if you follow QI), because you'll fall victim to CC if so. One way to combat this is to pack CC-resistant fast creatures (only Phoenix really applies here when unupped, but SoFree or Fractal can help too).
Optionally, you'll likely want some PC so as not to be slowed down by permanents either. Similarly, you might want some CC to stop things like Squids. In the end it's about being as fast as possible AND being hard to slow down.
That's all for now.