Hi anonymous...
The HP of the engine depends on you turning it to the recommended RPM. If you are low on RPM you have less power, simple enough.
Look in your Rotax Operator's Manual and they give you the RPM needed. Part of this is the type of aircraft and what type of flying you do. We don't know that so I assume your OEM has calculated these values already. Since you are dealing with a none turbo engine and your numbers suggest you are flying well over the normal pressure altitude this was designed for there will be some big variables.
First, 5100 sounds low as you must achieve at least 5200 on normal climb. The prop will unload as you roll down the runway and RPM will increase. On a normal climb you need to get over peak torque, 5200 and a bit higher is fine.
Second, do not be confused by the Rotax number of 5800 as max, that is achieved if you have a constant speed or inflight adjustable prop. With your fixed pitch you should see about 5500 at WOT in normal altitude density. This is generally considered to be about 7500 feet as I recall. The loading to 5500 allows for some increase in RPM if you should drop the nose pitch for some reason. That max 5800 RPM is for 5 mins only. Remember that the prop is your governor to control the load on the engine and not overspeed it
Just my opinion but you are overloaded on your prop pitch from the sounds of it.
Cheers
In general terms the prop unloading from less dense air will be about the same as the power loss of your non-turbo engine power loss. In most cases the RPM will remain the same from sea level to normal flying altitudes. The notable change will be your rate of climb will drop off proportionately to the loss of power. (about 1% per 1000 ft of climb)
In your number 3 note this seems way out of balance. It appears you are flying in very strange conditions. If you pitch your fixed pitch to fly in these conditions, unload the prop pitch to get 5500, you will be overspeeding your engine at the higher density on take-off.
