Before Punk Hazard, Law was in fact investigating Doffy. But there's no proof that he was doing so at all pre timeskip, this is headcanon. We also have to wonder why Law wasn't at all concerned with Luffy disrupting the event, nor was any flashback shown that Law had been trying to gain info on Doffy 2 years ago. You'd think Oda would have done something to show this if it was his intention, but all we currently have is your theory. If you admitted it, it would be less embarrassing
You are being entirely disingenuous about what Law said here. His crew was asking about going to the new world, not anything related to Doflamingo. Based on what Law said, his crew assumed they were after the one Piece. In fact, given the fact that Doffy is in the new world, we have to wonder how a human being could possibly think that Law would gain more knowledge hiding in the grandline. Maybe if there was some sort of traumatic brain injury? I don't know, but I feel a bit bad.
Also, I hope you do realize that Law didn't figure out anything great. Joker making a business deal with Kaido is not something people were ignorant of. Kidd's alliance discussed this. Law already knew who Joker was after the young master took the ungrateful shit in, so I'm not sure what opportunity Law was looking for in the grandline? We also know he only was able to become a warlord based on what he did in the new world. so
Damm, I'm not sure how you're struggling with the smile thing. Law smiling alone does not prove anything, what it proves is that he seems pretty comfortable in the environment, and is clearly not angry or enraged at what he's seeing. I think he's interested in the slave trade for a more important reason. Of course, you know as much as I do that him smiling is pretty strange behavior, which is why you said it was "his pretimeskip resting face" or whatever, but obviously that was too retarded to use as an actual argument.
What WG hate? If you want proof Doflamingo hates the world government, I could give it to you. I don't have proof that adult Law has any hate towards the government really, he clearly doesn't seem like he wants revenge on them nearly as explicitly as he wanted revenge on Doflamingo or Vergo
Again, I'm not sure if you're pretending to be dumb or are actually dumb. What do you not understand here? Oda went out of his way to make Kidd and Luffy's views on the celestial dragons and the slave trade obvious through dialogue. Law's view was kept ambiguous, if not indifferent. A lack of dialogue can say as much as an actual comment
Is Law's crew running and screaming because they're not grinning during the auction?
You can actually see the face of someone who doesn't want to be the auction or is uncomfortable, vs Law, who doesn't look like that at all.
I also respect the morbid curiosity argument more then the "well he was investigating the auction Doffy wasn't present at because uhhhhh", because it makes a lot more sense and actually makes a little sense
No, the single basic fact is that Law was at a slave auction, and the manga didn't really give us a reason why. What he did after Luffy ruined the event is almost entirely irrelevant
No, what someone without an agenda would say is that once Luffy derailed the event, Law decided to free a guy he thought was strong or whatever, and we never found out why he was there in the first place. They probably wouldn't be making goofy theories about investigating Doffy