These guys are correct, a disc brake conversion is a bit like a live axle conversion, it's simply not worth the time & effort...
From what I can see in the pics, the wheel hub is out of alignment; remove & inspect the hub & axle, look for spacers or anything which will impede inward movement of the hub; if there's nothing there, you may need to space out the sprocket & brake drum from the hub...
Adding to the brake issue, the band mounting pin is bent (see pic 4, post #20), which will throw off the band alignment; strighten it, making it square to the frame, & that may even solve the issue...
Seeing the amount of oil & crud in the vicinity is a bit of a worry, as you probably know, once oil gets into brake or clutch material, it's toast...
Larger tyres
will affect the drive ratio; have a read through
this, by the end, you should have a much better understanding of gearing...
A replacement throttle cable can be as simple as a trip to the lical bicycle shop for a brake cable & a couple of cable stops/anchors; determining the correct length before hand is the hard part...
All this can be a little overwhelming at first, just try to remember, a kart is just a small, simple car; however, adding posts incessantly every few hours can be considered rude; as this is a 24 hour forum, there are members signing in at all hours; for example, you're probably just about ready to go to bed but, it's the middle of the day here; Paul (landuse) should be here in about 4-5 hours...
All I'm saying is a little patience goes a long way. I don't respond to every thread but, I look at them (it's kinda my job
) & I'm not the only one; people will view a thread but, if they have no useful input, they move on...