In Star Wars and Star Trek they go to some strange planet without a bio/chem suit and no one pays any attention to it. However Covenant everyone throws a fit. Also not everything has to happen on screen, sure a throwaway line like "Walter has analyzed the environment and determined there are no contagions" wouldn't have hurt.
When Faris fires blindly and blows up the shutte, that's not hard to believe. You're being attacked by who knows what and it just tore apart someone. You think you're going to stop and think...wait I'll let it tear me apart and not shoot at the damn thing.
As far as them getting picked off and going off solo after David brings them to the Citadel. You could say that David saved them and he said the location was safe, so they thought the location was secure. Remember he's an android and they have no reason not to trust an Android based on their experience....I myself would of split into two man teams and did a security sweep, but most of these people weren't military. We as an audience know it's an alien movie and shit is going to go bad. We need to try and look at things from the perspective that they have no idea what's going on. If you have ever been in a combat environment you know people don't always act rationally when under stress and pressure. Hell even in training with sim rounds I've seen people make very bad decisions and go into full panic mode, and they know these aren't live rounds being shot at them. The final point, it's a movie you have to suspend your belief to a certain extent. The choices that were made I didn't think were so far out there that they couldn't happen in real life.