Ross probably already has plenty of answers to the questions by now, but I'll throw in my own. I'm a die-hard fan of the 2D games to this day and loved the Adventure games and Heroes when they came out, but everything afterwards kind of lost me, so my answers are gonna be molded by those games and not really anything afterwards.
1.) In CD and Adventure, Amy was more portrayed as a "fan girl". The kind that'd obsess over a boy band, fantasize about a relationship with the members in it but not really think about it seriously. In Adventure 1 a moment that solidifies that is that she uses Sonic to get into the theme park level for free when he's supposed to be protecting her, then runs in so fast Sonic loses sight of her, and then when she realizes she lost Sonic afterwards she doesn't care that much. Heroes is the game that fully Flanderized her into practically a stalker and it became her only purpose in the plot. I've heard this has been at least partially reverted in newer media, dunno how true that is.
Additionally in CD I get the feeling they don't even know each other at that point, and there's not really a mention of marriage. It is kinda weird in Adventure just because they clearly know each other by that point, but generally I think "star struck romance day dream" is more accurate to her old character.
2.) The Liquid Metal Sonic is a lot of very weird specific, convoluted lore just to explain that one cutscene, but it is actually explained! Chaos' DNA (from Adventure, he is a water god thing) is on the Team Rose's Chocola and Froggy. Chocola because Chao are like strange off-shoot breeds of Chaos, maybe his children? And Froggy because in Adventure 1 he swallowed Chaos' tail. So they just both have Chaos DNA. Sonic kidnapping the two in a newspaper was actually Metal Sonic, infusing the DNA let him use Chaos' powers (becoming liquid, and I guess shape shifting). The DNA is also what makes him go rogue and rebel against Eggman and then pretends to be him.
It's a weird plot point. It can't really be called lazy writing because of how takes a ton of really obscure minor details and ties them together kinda coherently? But it's simultaneously just an excuse to make Metal Sonic T-1000 between places and have a bigger eviler bad guy at the end while keeping Eggman through the rest of the game. I dunno, it's weird.
So yeah if I had to guess, Eggman doesn't make more robots like that because he doesn't want Sonic Heroes 2 to exist
3.) Tails is based off kitsune legends, so that's why he has two tails (and also probably why he's super intelligent). So while the anatomy question is legit... if we go by the logic that Tails is a literal kitsune, then you're also questioning the supernatural and the unknown. (...Basically, this is an excuse to skip this one :V)
4.) You're spot on with your assessment: ever since Adventure 1 he's had dialogue talking about destroying cities to make room for Robotnikland. (A level in Sonic Unleashed even takes the idea and turns it into a level). So his end-game is literally just to rule so he can put his face on everything and be able to say he owns the planet. He definitely doesn't seem that interested in governing, but he does want people to follow his every command too.
I wanna add Eggman also is the sole proprietor of the Death Egg. That makes your point even crazier; he matches the raw power of the Empire from Star Wars (or arguably exceeds, with how fast he repairs the Death Egg twice in Sonic 3 & Knuckles) ... as one single man. The Sonic universe would honestly not be able to do anything without Sonic there to stop him, this one hedgehog is the sole reason he isn't able to get away with doing literally anything he wants.
Even more, his dialogue in Adventure 1 differs between each character. When you're Sonic, he has his absolute cheesiest lines and goofiest deliveries, and Sonic just makes fun of him the whole way through. As any other character, even during scenes that they witness with Sonic, you get different dialogue with way more intimidating delivery. It paints a picture that Eggman is a terrifying force, just that Sonic is only one who doesn't take him seriously.
5.) I think the main argument for Knuckles not being a vampire is that he can exist in the sunlight, but then again, there have been stories where they just get weaker in sunlight. But then again again, that means he probably wouldn't be able to maintain his Super form like that outside if it weakened him. Data inconclusive.
You don't get to see Vampiric Knuckles in 3D unfortunately because Super forms were retconned to be "only male hedgehogs can do it". Which is super (tee hee) lame.