Because the battleship only appears in Stage 2, thanks to your future self teleporting it and himself. You don't actually encounter the battleship until the end of Stage 7, but you know how to destroy it due to the events from Stage 2 and the analysis of the battleship by your ship's computer at the end of Stage 7. So, in a way, you have already completed the game at the end of Stage 2.
Can you please clarify? You haven't addressed the "two players" part. The way I see it, two ships traveling together (as in a 2-player game) could've drawn the same conclusion about the enemy ships' weaknesses from the scan ("This requires two ships? Hm, this is a two-ship squad...") and then split up to destroy the ship without having to time travel to double their forces.
Exactly what did Bacterion mean when he said he was born from the greediness of mankind?
Presumably that means that the Humans created Bacterion - It's a bit ambiguous, really.
What happened to Venom between James activating the Shield Device in Nemesis 3, and him becoming the brain in Gradius V?
It's possible that the brain you see in Gradius V is a different Venom. It's either that, or between Nemesis 3 and Gradius V, Venom was assimilated to the Bacterian Empire to become the new Hive Mind.
Why does almost every time as you get close to the Big Bad in his fortress/planet, things look organic?
Because in the depths of the final fortresses, we can see that Bacterians power their applications through their own abilities, meaning their very organisms themselves can provide power to whole fortresses / forces / armadas
What's with the faces surrounding Bacterion?
Bacterion is a Hive Mind. The Faces are probably just the many different bacterian cells that compose him.
But the faces surrounding the final boss of Gradius Galaxies....
What's the point trying to destroy the Bacterians when there are so many of them that it's impossible to kill them all?
Eh.. good point. Maybe it's because it slows them down for a few something years before they attack again?
Because it's not worthless. If it was, how could Gradius Gaiden take place in a world hundreds of years in the future where the people have forgotten what war is like?
The time it takes for the Bacterians to recover varies a lot depending on how damaging the defeat is.
In canon there's currently no way whatsoever in completely deleting the Bacterian threat, and indeed, the last boss of Gradius V stated that shreds of them will be spread each time they're defeated, only to come back in exact measure of strength. With the factor of them becoming stronger through time, you get yourself a galactic version of a human body imperiled with HIV.
Gradius NEO, set very far into Gradius's future, suggests that the Bacterians are eventually dealt with permanently: they're still around, but they've failed to rebuild their intelligence and are basically just animals, harmless to technologically advanced society. The new enemy is instead a human civilization (the Lars Empire) that is using old Bacterian tech as Lost Technology.
Here's the story of Nemesis 3; Venom and Gofer (or Gofer II) travel back in time to year 6644, start the Northern Cross War, the real first Bacterian attack (not the Bacterian attack in Gradius 1) that ends up with most of Venom's race indirectly killed, and kidnap a three-year old James Burton and hold him prisoner so he won't grow up to be the Vic Viper pilot that thwarts the Bacterians. So David Burton, a future descendant of James, goes back in time to defeat the Bacterians and save James. But here's a thing that's bugged me: since Gofer II was killed in 6644 and, taking in account the Bacterians being a form of The Virus, doesn't that mean that pieces of Gofer II would become sentient and become a new Big Bad that would return to attack Gradius?