Can I place all 4 cards that I looked at with the Trainer card "Research Record" at the bottom of my deck? Or can I place all 4 cards on top of my deck?
Yes, you can put as many of the four cards on the top or on the bottom any way you like (except face-up).
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)