identify the type of reaction that occurs between potassium carbonate and nitric acid

Answer 1

K2CO3 + 2HNO3 --> 2KNO3 + H2CO3 then the H2CO3 decomposes as
H2CO3 --> H2O + CO2
I would name that first reaction as double replacement.(some call it double displacement).
Usually this reaction is written all at once as K2CO3 + 2HNO3 ==> 2KNO3 + H2O + CO2 and that makes it a little harder to see it is a double displacement reaction. It could also be called an acid/base reaction. As such the net reaction is
CO3^2- + 2H^+ ==> H2CO3 ==> H2O + CO2