TenForward: Where Every Vulcan Knows Your Name

Hard to say. There was direct Romulan meddling in the Vulcan government in the fourth season of Enterprise. Some people on both sides certainly knew, but it probably wasn't widespread knowledge.

Romulans didn't need to be taught. They were always technological equals (possibly superiors if you count cloaking). Yet instead of making amends with an equal, Vulcans chose to embrace the neophyte humans and grow them to technological equality instead of embracing their brother and sister Romulans.

Humans are space orks.

They both seem pretty well assimilated into human culture though. Maybe the crazy can rub off. I think the Vulcans definitely would have said that about T'Pol.

In actuality though, I think it's probably just that every species has these people, humans just have more for whatever reason. And so the other species' people go to join the humans

Why do you think there are so few Orions in Starfleet? Because Tendi is one of the few weirdos who Gets It. The rest are like "WTF you people are crazy!"

"Wait, what do you mean humans do not have a breeding season? Then when do they breed? ..Always? Get me the Vulcans on screen!"

Your comment and the OP act like the Tellarites don't like anyone, but that's not really true. The Tellarites and Vulcans got along just fine before Humanity showed up. The Vulcans probably figured out the Tellarites' gimmick and decided that challenging each other's ideas was how they arrived at a logical conclusion. The Andorians were probably too hot headed to get along with people who challenged them on everything, leading to them being in conflict during ENT.

As for how humans fit in, humans may be crazy bastards, but they also occupy a nice middle ground between the others. We can be as emotional as Andorians one day, as logical as Vulcans the next, and a number of our political systems were built on Tellarite-style arguing. Humans can hear out one ally, then explain their position to another in terms they'll understand. We can also tell when Vulcans are secretly being driven by emotion, can leverage Andorian emotions to bring them to a more rational perspective, and debate Tellarites on even ground. Humans are the interpreters and negotiators that got these people to actually talk about their problems with each other and come to a reasonable compromise.

The Federation is created at the end of Enterprise: before that there's a cold war going on between the Andorians and the Vulcans. The Coalition of Planets forms during the show and is dissolved when the Federation is created.

Well, the whole point of a diplomatic interplanetary body is to have a common forum of communication to soften their relationships over time, by allowing dialogue and cooperation to occur at some level in a fashion doesn't involve shooting phasers and photon torpedoes at each other. Even if the shooting still happens from time to time.

It's a parallelism with the UN. All sorts of countries who hate each other are part of it and sit at the same table, at some unequal level even. They still shoot each other and commit atrocities towards others and their own people from time to time. But still, the point is that the table exists and is available. It creates opportunities for dialogue and cooperation, that wouldn't exist otherwise, that create opportunities to solve conflict peacefully and soften their differences over time.