No you worry about civilization culture and democracy, else what's the point of the survival of the species. Remember no government has ever voluntarily given up power, if you decide you now have a 100% military society to deal with the crisis then you've decided you will have a 100% military society until there's some sort of revolutionary war that ends your current government.
Cylons are no better at lying than people. We interrogate prisoners of war because we hope to see through the lies and find useful information. Away from the resurrection ship Cylons fear death just as much as people and experience pain and are social creatures that don't seem to like isolation, those are the primary tools of interogation of people too.
They had no way to know how long the Cylons would remain disabled, they'd already seen that raiders would pretend to be disabled to gain advantage. Also by that point that had a captured raider and a captured stealth Cylon. And what happens when a raider captured because it was software disabled finds a way to reboot and you've got it INSIDE your ship?
They didn't know Baltar was a Cylon sympathizer. And really Baltar isn't a full on Cylon sympathizer, he's a tool (in the most insulting use of the word) who's wound in love with one Cylon model, most of the time Baltar is just a self serving jackass. They made a decision that it was to be Baltar's test, the logic was that if they couldn't trust Baltar they were screwed anyway. Maybe not the best logic in the world but since he was the only surviving scientist they had it makes sense, they had to trust Baltar so they decided to trust him. If they didn't trust Baltar they weren't going to get a Cylon detector, if they trust him and he doesn't deserve it they weren't going to get a Cylon detector, if they trust him and he deserves it they get the detector. They had to trust him, and hope.
No Rosalind was right. For one thing the Colonial government had surrendered, and for another they had nothing to seriously continue the fight with. Adama was looking for a suicide mission, wanted to go down fighting and feel in his last moments like he'd done everything he could. But Rosaline pointed out that path was silly, what he could do was protect the remaining civilians in the hopes that they'd find a way to re-establish and rebuild. No sacrificing the last 50,000 people in the universe on a fools fight you can't hope to win is STUPID, taking the one slim chance for survival of the species, which is what they did, is the ONLY smart move.
There's an idea. The humans just have to get their "boxing" technology. We know the Cylons are very afraid of that, so just put them in the box and pull them out every couple weeks until they talk. Or maybe it could be mimicked with a sensory deprivation chamber.