Hello!

Sorry for the late reply. 

For the rate law, it can include the concentration of MnO2 which is a catalyst. 

You can write the rate law as you said : Rate = k[H2O2][MnO2]

But for the reaction order should be investigated with respect to H2O2 and MnO2. I don't know if they have first order, respectively as you stated. 

Why is the concentration of MnO2 included?

The concentration of catalyst does not change throughout the reaction, thus [MnO2] stays the same too. 

It can be writeen as Rate = k[H2O2][MnO2] or Rate = k'[H2O2] where k'=k*[MnO2].

Additionaly, MnO2 is not a manganese dioxide, it is manganese(IV) oxide. 

It is an ionic compound which has no prefixes in naming, and Mn is a transition metal which requires roman numeral for its charge. 

I hope it helps. 

Thank you!

Kelda