As Sam walks through the compound door carrying the case, the exterior shot shows Sam carrying the case vertically by one of the end handles. The subsequent interior shot shows Sam carrying the case horizontally by the side handle.
When Michael and Fiona are evaluating the hostage site, they use a thermal imaging camera to view the house and are able to see the interior. Infrared energy does not penetrate walls, just as light energy does not penetrate walls. Thermal imaging cameras cannot see through walls. (In fact, thermal imaging cameras cannot even see through glass, as glass reflects infrared energy and therefore glass acts as an infrared mirror.)
Under no circumstances would a guidance electronics engineer like Resnick have need of a Bunsen burner in a lab with an already-constructed missile casing. And soldering of circuit boards is never done with open flame.
When Sam and Jesse go to the lab where Resnick is hostage, Resnick tells Jesse that his daughter was kidnapped. There is no way that Sam could have overheard their conversation, and no way that Jesse could have relayed that information to Sam. In the next scene when Mike and Sam are talking to Pearce, they all know about Resnick's daughter.