RE: How much does altitude affects engine power
The thing that looks strange to some people is the fact, that when the air is less dense, the engine uses less fuel and makes less power, but the prop is spun at about the same RPM, as it does at sea level.
The thinner air also affects the load on the prop, allowing it to spin faster with the same power and at the same speed with the lower available power. Aircraft performance, however, is directly affected by the power, not the RPM.
Real planes with S/L turbocharged engine(s), make the same power, to 15, or 20 thousand feet, but still take a longer runway to take off and land, because lift is also a function of air density and more speed is needed to take-off.
The IAS will be the same at take-off speed, but the TAS will be higher.