It is Merry that speaks up at the Gate, and Merry that instructs them to mind their P's and Q's in the common room (in my quotes above)... I think our Frodo is still lost without Gandalf, not taking any charge, he is still a passenger on the quest....
Yes, Merry is still the leader. Is it because as a Bucklander he is more familiar with Bree and Bree-folk, or is it because Frodo is more withdrawn with his worries about the quest and bringing his friends into danger?