Starbuck killed Leoben with a pair of chopsticks. Metal ones, I think. RDM refers to them as chopsticks on the podcast.

Why couldn't they just check the drawer instead of watching for the upside-down food dish?
I wondered the same thing! But only thought is that they since both the informant and the resistance fighter want/need to remain anonymous, they can't risk running into each other at the drop-off site. Though....couldn't they just as easily run into each other at the dog bowl? Eh, *handwave*