Although probably not technically correct, in common usage we'd say "I'm not making pasta now". At least in the UK we'd say that and understand "making" to mean "cooking".
Well, we've added "make" to "cooking soup", so I guess it works here as well. Added.
If it was explicitly put in the sentence, you have to translate it.
Besides, it could potentially be Present Continuous in the future meaning. Like "On Friday I am cooking pasta".
Maybe in the right context.
The distinction between present continuous and its counterpart (I can't think of a name for it) is not so precise in English. For example, we say, "I cook pasta" but we say "I do not cook pasta" instead of "I not cook pasta" even though "I do cook pasta" has a different meaning.
"I am not now cooking pasta" was rejected. any reason for that? I am a native American English speaker and it sounds perfectly normal to me.