Some ideas
oh yeah as to the vase, not quite sure, but it was moved along with the laptop. If something was in the vase i think Conan would have noticed (on account of him examining it for hours for an appraisal. They may have moved it and put something in it or under it, there is a possibility they would leave something to monitor them with (Conan). Maybe that Vase is still important, maybe the person to show up to appraise it has a connection with the kidnapping? not sure about this though, i will need more evidence to narrow this stuff down