The H2O2 motor works by the heat and pressure of the H2O2 decomposing. Both of you are correct. It is a monopropellant, but it does go to water and oxygen. I however see no reason why you couldn't inject a flamable fuel in with the products to produce even more thrust.
I'm sure there is more than one type of rocket that uses H2O2 as a propellant, or part of the propellant. I have heard of H2O2 and liquid methane I think it was.
Thrusters and motors are completely different things. You can have peroxide thrusters when you have got to orbit; i.e. to change your attitude with agility and to make very slight changes to your orbit. But it is actually physically imposible to rely on a H2O2 thruster to get you into space.
The energy density of a peroxide decomposition thruster is that low, that the mass of the fuel required to get a rocket to space is more than an order of magnitude greater than the mass of the rocket itself. H2O2 on its own is not a viable way to reach orbit, or 100km for that matter.