“pan.” The Hebrew is a rare word, maserath (#04958 מַשְׂרֵת), only occurring here in the Old Testament but well attested in post-biblical Hebrew. There is no reason not to believe that shallow pans would have been available, especially among the king’s household, for specialty baking.
“and set it out.” The Hebrew text is unclear here. For one thing, there is no object to the verb, “it” is supplied. The act could be that she “set them out,” “poured them out,” “dished them out,” “set it [the pan] out” etc. What she actually did we cannot tell from the text. It is also possible that she is somewhat suspicious, because she seems to be keeping her distance and not feeding him with her hand, as he seemed to have wanted.