I have only skimmed a few posts on the first couple pages, so forgive me if what I say has already been said before.
We have no idea what the lifespan of the cogenitors are. They can be anywhere from a human lifespan to a Vulcan one... or even an Ocampa. If they do indeed live very short lives, it makes the impact of losing one felt even more. Considering that they are completely essential for the Vissians' procreation, there should not have been any intereference.
Do I agree that cogenitors should not have names or an education? Absolutely not, particularly since they are so essential. I would think they would be sort of revered.
Do I think Trip should have stayed out of their business? Absolutely. As a Starfleet officer on their first deep space exploration mission, everyone on that ship is representing the human race. How they go about first contacts are what's going to influence generations of other species when they encounter other humans. Trip was right in asking questions about their society and the cogenitor... that's how we learn. But he should NOT have been actively teaching the cogenitor. Particularly in secret... this means he KNEW what he was doing was going to cause massive trouble. Had he been upfront with Archer when he returned from the sun or even with T'Pol and let them come up with a solution, my opinion of the outcome would be vastly different.
Do I think Trip is at fault for the suicide? Yes. While it's true he could not have predicted the suicide, that's precisely why he is at fault. We only have our own species as a barometer of knowing what kind of reaction would happen if the cogenitor wouldn't get asylum. Because the Vissians are an entirely new race, there are no frames of reference to predict any outcome. Which is why it wasn't up to Trip to teach Charles. You can't apply human standards and morals to an alien race. He is definitely the one at fault.
Is Archer at fault for the suicide because he didn't grant asylum? In this case, for the very same reason Trip IS at fault, Archer is NOT at fault. Archer had to basically clean up a huge diplomatic mess Trip created. Trip was only thinking of one person, while Archer had to consider consequences for his entire crew, the Vissian couple, the cogenitor, future relations between humans and Vissians, AND the fact that this single cogenitor could seriously affect the reproduction of thousands of others because they are so rare. While I wish a better solution could have happened, Archer did the only thing he could do at the time. Maybe as relations got warmer and more frequent they could address it with the Vissians to give some social reforms, or even help them come up with a medical alternative. Frankly, they were incredibly lucky the Vissians were as friendly and reasonable as they were, or they could have easily destroyed them and targeted Earth and destroy everyone just to make sure humans won't meddle with their affairs again.
To be perfectly honest, given the severity of the situation, Trip should have lost his commission. If it were many years later, he definitely would have. In this era, he should have been dropped down a rank to Lt. Cmdr., with a reprimand that will take him a long time to get his rank back. (Even though we don't see on screen evidence of this rank, I seriously doubt it didn't exist, for the simple reason of Starfleet being based on Naval ranks.)
In short, I think Archer let him off easy.