What is the rate expression for decomposition of $\ce{H2O2}$ in the presence of a catalyst?
For catalase, it is most likely Michaelis-Menten kinetics.
At typically low enzyme concentration, this would be first order in catalase. For hydrogen peroxide, it is first order at low concentrations (&lt;&lt; Km) and approaches zero order at high concentration (&gt;&gt; Km). This behavior is also called saturation kinetics.

I don't know what it is for the catalysts $\ce{MnO2}$ and $\ce{Fe2O3}$. Another question in my mind is that even if it's similar to that of catalase, since these are powdered and so do not have a concentration, how can I express it?

For catalysts in the solid phase, it is the surface area (compared to the volume of the solution) that matters. You might see similar saturation kinetics, indicating that at some concentration of reactant, all the surface area is used so that an increase in reactant concentration no longer translates into an increase in rate.