A sing vs a maker in this context

Hi,


Excuse me for being so greedy but I have three question and they are in the same paragraph down below.



1) Is there any difference between a sing and a maker in the context?



2) What is the meaning of this "knock ourselves out"? Like, working hard?



3) What kind of "as" is this?




(This is an excerpt from Me Talk Pretty One Day by David Sedaris, and Agent Samson is actually a speech teacher.)


"One of these days I'm going to have to hang a sign on that door," Agent Samson used to say. She was probably thinking along the line of SPEECH THERAPY LAB, though a more appropriate marker would have read FUTURE HOMOSEXUAL OF AMERICA. We knocked ourselves out trying to fit in but ultimately betrayed by our tongues. At the beginning of the school year, while we were congratulating ourselves on successfully passing for normal, Agent Samson was taking names as our assembled teacher raised their hands, saying, "I've got one in my homeroom," and "There are two in my fourth-period math class."



Thank you,

M