Few unanswered posts here. I’ll take a stab, but definitely defer to those with more experience and keener eyes if they chime in.
1) the 329.32.44.51.01.001 Speedmaster Racing: looks good to me.
2) Re: confirming the serial number for the 3861: you can go to Omega’s website and join a chat with a rep. They might (or might not) be willing to confirm that it’s a real serial that belongs to that model. Depends on who you get and what mood they’re in. I wouldn’t expect them to give you any more info than that, though. And just confirming that it’s a real serial doesn’t mean it’s a real watch. Could be a clone of a real one that kept the same serial. Buy the seller, as they say, and do your diligence.
3) Re: the Planet Ocean chrono… fake as a $3 bill.
4) Re: the 2541.80 Bond watch, I’m not seeing any obvious tells, but this was a commonly faked watch. Since it’s also such an easy reference to find, I’d urge you to buy one from a seller you can have supremely high confidence in. A place that checks for and guarantees authenticity. (Joma, Crown & Caliber, etc.) Just to be sure you know: this is a quartz watch, not an automatic. (That too makes it somewhat easier to fake.)