*In order to really understand this Answer, one must absolutely dedicate 19 seconds to watch the Dr. Who trailer.
Scene: Creepy music. Anima-reality. Sharp lines. Dark shadows.
Dr. Who: Clara, be my pal and tell me... am I a good man?
Clara: I don't think I know who the doctor is anymore.
Be my pal and
do something. (Replace
do something with any common small favor.)
This idiom is an exhortation to do something. The core meaning is the imperative
do something. The "be my pal" part is completely rhetorical. (The implication is that if you
do something you are considered to be "a friend" but if you don't
do something then you are not being a friend.) Being rhetorical, it can be used in contexts that are ironic or otherwise not completely sincere. Also, it's extremely informal; it's typically used for relatively small favors like "be a pal and pour me another (drink)", "be a pal and help...", "be a pal and give me a hand".
It's based on be a pal and
do something. See Google Ngram: be a pal,be my pal,be a pal and. It's practically identical to the more common "do me a favor and
do something (NGRAM link)", though the latter doesn't have the same level of rhetoric. Also, compare with, "Would you (please)
do something?" which would be a sincere and standard way of asking someone politely.
This is, after all, the premier line of the trailer, and it smartly functions like the climax of a story. The line is well crafted and complex. The intonation by Dr. Who is subtle yet tangibly creepy. The register of "be my pal and" is informal and rhetorical which contradicts the more formal and supposedly sincere "am I a good man?"
One must conclude that Dr. Who is absolutely not asking Clara to be his pal and neither is he being sincere in asking her if he is a good man. Everything is a contradiction. His question, his tonality, his character, his relationship with Clara, and the situation. It all points to an atmosphere of danger; it's dangerous to even answer this question.