That engine is a very nice revision of a Chrysler 3 cylinder engine and runs remarkably well for its design. The problem is that it still is dirt common crossflow design. Yes, the OMC 50 loop charged engine will be competitive.
The gearcase is the small Mercury gearcase used in the 30, 40, and 50. You can use some Mercury props and yes, the correct prop is a 10 inch diameter prop.
NOW--As to whether or not a 13 pitch will be faster, MAYBE. Right now you are running 4800 RPM. The 13 pitch should raise the RPM up to about 5200 BUT--the decrease in pitch may still result in a slower top speed. Great hole shot though.
You really need to check compression ratio to be certain the engine is healthy. Then you need to experiment with props--and yes, this can get expensive. You might also consider a stock Mercury 15 pitch stainless prop which SHOULD (not will) give about 200 RPM more than your aluminum
You need to also maximise the engine height on the transom and weight distribution in the boat. If the engine does not have power tilt/trim you need to find the best position for the tilt bar.
Again, comparing your friend's 50 to your 75 is comparing apples to oranges. His hull may be lighter with less wetted area and his set-up may be optimised for maximum speed. Also, he may be a small 150 pounder and you may be a 300--makes a difference.