How does malachite react with acid?
No, pure malachite $\ce{Cu2CO3(OH)2}$ usually doesn't produce hydrogen because it is a copper carbonate. Copper is already in a higher oxidation state (+2) so it can't reduce hydronium to hydrogen. The right reaction is the following:
$$\ce{Cu2CO3(OH)2 +2H2SO4 -&gt; 2CuSO4 + CO2 ^ + 3H2O}$$

However, if there are traces of metallic copper some hydrogen can be produced but not with sulfuric acid because:

$$\ce{Cu + 2H2SO4 -&gt; CuSO4 + 2H2O + SO2 }$$

Nor with $HCl$ (copper doesn't react with $HCl$)  but only with nitric acid or aqua regia you can produce hydrogen from the metallic form. So, in fact, the gas you see is carbon dioxide.