Yes, in agreement that it appears to be home-made. By and large most commercial go karts are made of round tubing, not square, so that is one of the dead-giveaways. It is well made however and something to be proud of.
More pics please, especially of the engine.
I like the combination belt and chain drive. Is that a TAV (Torque-A-Verter) or just a clever jackshaft assembly?
Sure, take out the governor and follow what
JimD says OR
adjust the governor to deliver a higher RPM than stock. If removed, don't be a fool and rev the ever living piss out of it, you want it to last a while.
Honda GC series is cool. One of the very few small engine lines that has an OHC (overhead cam) run by a belt drive (just like modern automobiles). Good that the builder dealt with the "wrong direction" exhaust port by routing the exhaust to the rear. It's not crazy that it is front-facing on a Honda GC, just different.
For the quietest muffler, the sky really is the limit in regards to what you could cobble together and/or weld up. What is the pipe's OD/outside diameter? If it is 1" I could suggest a simple Briggs "wiener" muffler [
Briggs & Stratton #294599 ] but you'd need a threaded coupler which is 3/4" NPT (or just have it welded onto the end of your pipe). The outside diameter is about 1" and it could be butt-welded onto the end of your pipe but a threaded coupler would allow it to be removed at will.
If the pipe is 1" OD, another option is the RLV Mini 91 slip-on silencer (needs a clamp) but it may offer less noise reduction than the Briggs mentioned previously. Not sure.
Ultimately, I'd ditch the GC engine and go for a.... Rotaderp (read it backwards) and join the rest of the crowd. Lots of performance parts are made for them and the know-how is available at your fingertips.