I think Asuma and the 3rd discussed with each other and weren't in good terms.

The translation states Asuma thinking about a few words the 3rd said to him, that it wasn't good to only do things you like, and detach from everything else.

For a moment I thought the monk was another jinchuriku.

A guard monk of the feudal lord, in the bingo book.
I guess not only s-class criminals are on that book.