I am not native enough for this so I will just leave a link to ngrams here: https://books.google.com/ngrams/graph?content=Have+you+a%2CDo+you+have+a%2C+Have+you+got+a
Why not "Do you have any pears" this means the same, but is better English.
I put "do you have a pear?" and it said I was wrong. why is that?
Hrušky is plural (accusative case), so pears. Hrušky could also be singular genitive, but genitive is not possible here.