Since we are not there with you, it would be good to have photos of everything you have. I had no idea you had the brush guard.
Count the teeth on your wheel sprocket and that will determine what kind of clutch to get.
Looks like it uses #35 chain (I see some chain on the floor) but verify with the included guide
Kart is one wheel drive and is ideal for what it is. Larger tires will only complicate things.
Looks like you do need a new brake band for the drum.
The Fun Power engine is an excellent engine, very reliable. Does it seem okay? The only warning sign I see is that it needs an air cleaner assembly on the carburetor.
