How big is the population? That is not a good sentence in English. Because it is unclear if it means what is the population? (i.e How many?) or How big or tall is the population.
The usual way to ask the question is what's the population?.
I disagree. That's like saying 'what's the population' is ambiguous because it could mean population or e.g. make-up. 60 million, 50% ethnic or human would all be valid responses. I think if you asked 'how big is the population' the overwhelming response would be a number and not a height