It is mentioned that "Ask a well-received question on 30 separate days, and maintain a positive question record". So does it mean that on 30 separate days I have to ask different questions and all those questions should have +ve score?
Yes, but this is not enough.
Indeed, a well-received question is one with positive score; it also has to be open and not deleted to count.
However, and possibly counter-intuitively, for a day to count for the 30 you must not have asked any question that is not well-received on that day. In other words, only days where you asked a question and where all questions you asked were well-received count towards the 30.
Finally, as said in the description, you need a positive question record. This takes into account all questions you ever asked, not only those on the 30 days. What it means exactly is explained on What is a positive question record? (also see Why was the "curious badge" badge not being awarded?)
Moreover, List of all badges with full descriptions contains details for all badges.