A couple of other quick ideas: humor, relationships, and being really firm. I've found that it's huge to know how to really quickly switch between these three modes - how to be very firm one minute, but be really funny the next, and then switch to being more caring/supportive. It's all about timing of course, but I've found that a lot of teachers that get in trouble in more urban schools often don't know when to be which. They're mean all the time, so they lose respect and destroy relationships. Or they're caring all the time, and get "trucked."
Yeah, with something like the "I'm not singing, I'm humming," I'd be tempted to say something funny in response, "Very interesting, could you demonstrate singing so we can tell the difference?" but not in a sarcastic or mean tone, just a funny tone. Of course, that assumes you've also spent some time laying down the law, and some time really getting to know your students.
Also, I read through a couple of your examples, and most seem to involve the student attempting to avoid punishment or deflect responsibility by highlighting the behavior of another student. If that's a big issue, I might consider a brief 10 minute social skills lesson where you teach accepting responsibility. Then, if a student tries to deflect, prompt acceptance, then reward (even just verbal praise might work). You could also say that if responsibility is accepted, there will be no consequence, but if responsibility is accepted, there will not be (with minor infractions). Teach that an acceptable response is, "You're right, I'm sorry."
Tell students for the first week in your plan, you'll give one prompt - if they convert their behavior to the correct response, no penalty. If not, penalty. Tell them during the second week they'll only be given one prompt per period, but after that will be expected to respond appropriately without a prompt. For the third week, 1/2 penalty will be given if behavior is converted after first prompt. 4th week full penalty given even with no prompt.
Consider a similar procedure for other social skills if it might be helpful too