First of all, I think the sentences would be improved if you moved the word now either to the beginning or to the very end:
(1) I am not cooking lunch for anyone now.
(2) I am not doing what you want me to do now.
(3) Now I am not singing to my friends my favorite songs written by my uncle.
However, the word now in such contexts has an ambiguity problem. Let's take your lunch sentence:
I am not cooking lunch for anyone now.
That sentence could be describing two situations:
(a) You formally cooked lunch for people, but you're not doing that any more (perhaps you got a new job, for example)
(b) You're not cooking lunch at the moment (you will be cooking lunch in an hour perhaps, or maybe you finished two hours ago, but as of right now, you are not cooking lunch for anyone).
So, you could get replace the word now and with a phrase that more accurately describes what you are trying to convey.
(a) I am not cooking lunch for anyone any longer.
(b) I am not cooking lunch for anyone at the moment.
So, for Sentence 2:
(a) Right now, I'm not doing what you want me to do. I'll get started on my chores in a minute.
Or:
(b) I'm no longer doing what you want me to do. I need to start living my own life for once.
I think you'll find phrases like no longer, any longer, right now, or at the moment may be easier to place in a sentence.