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If I was sleeping and I just woke up, is it correct to say to someone:
How long I have been sleeping?
Secondly, the present perfect continuous implies the continuity but does it mean that I am doing only this activity? Like "I have been working this for two days" there are on and off.
How long have I been sleeping? is grammatically correct, but not what I, a US English native speaker would probably say. (How long I have been sleeping? does not have the correct inversion to be a question.) I would probably say How long was I asleep? or maybe How long have I been asleep? or even How long was I sleeping?
There just isn't really any reason to use the present perfect continuous here, because you're not asleep anymore.
Secondly, the present perfect continuous implies the continuity but it doesn't mean that I am doing only this activity? Like "I have been working this for 2 days" there are on and off.
I'm not sure if I understand your question correctly, but no, the present perfect continuous does not necessarily imply continuity or doing only one activity. You have to use some common sense and context. For example,
She has been working on her novel for four years.
I don't think anyone would assume that she has done absolutely nothing else for four years, only that the working has gone on during that span of time. On the other hand,
They have been arguing for an hour now.
certainly makes it sound like they have been arguing continuously for an hour without a break.
