Good Job!
I have been lurking on the forum for a bit ... really following your build and one other right now. My experience with the first test ride of our Tarantula variant was not too different from your yours, though some of the stuff I needed to fix was discovered when I just had a rolling chassis -- before my engine was installed.
"1. The throttle return spring I added did not work as I intended..."
That sounds like it was a hassle, sorry about that. I put my throttle spring on the cable between the clamp on the engine that holds the end of the cable and the wire-holder nut attached to the throttle arm. How did you have yours arranged?
"I think it might be too fast at 20mph"
I built mine to have a max speed of 36mph, using this forum's calculator. That was spot-on as we can get the cart up to 38mph going downhill on our road (and I think that it doesn't go faster because the engine actually slows it down). Anyway, after about 10 rides around our neighborhood (on the streets - I know, it's illegal) my boys were asking if it could go any faster. My boys are 11 and 12 though. My recommendation would be to somehow just limit the excursion of the gas pedal until your son's asking for more speed, which won't be long.
"The steering is not great. It does turn, maybe I expected too much. I noticed some issues with the right front wheel not getting full contact with the pavement when turning left. I might not have bent the spindle back far enough after it got damaged."
I had similar issues with my front-end. (It's good to realize that everyone on the forum has similar issues on their first build) I had to eventually cut off my spindle brackets and use a wooden jig to hold pieces at the exact right height and at the exact right angle to get my caster, camber, king-pin angle, etc. symmetric. And, as FabroMan says, trying to set up proper Ackerman helped me quite a bit. Using the jig was key.
"Very little clearance between the rear sprocket and the ground, not a problem on pavement, but it bottomed out going from grass to the driveway, so just need to avoid doing that." -- is there any way to use a smaller sprocket on your clutch and a smaller one on the axle? You could also try and construct a jackshaft above your live axle, have your engine drive that and then that drive a much smaller chainring on the axle. Probably all too much work though...
"The cable also frayed some and that was causing issues with it sticking in the cable housing, so it needs to be replaced." I've already gone through a cable for similar issues ... got frayed with me adjusting and re-adjusting.
"All the cables, springs and rods for the pedals make for too much going on around your feet. It's not as bad for my son because his feet are small." -- still, it's a huge annoyance! I had the same problem that I fixed (somewhat) by using bolts in my pedals to offset the control rods to the inside of the kart to get them out of the way of the heels of our shoes. I'll take some pictures and post here later so you'll see what I did.
"8. I have a kill switch ..." -- the kill switch is key... I wouldn't let my kids ride on the kart without one (being worried about setting up the throttle wrong or something and having a run-away kart).
"I'm not too upset with the results from the test drive, I knew there would be bugs to work out. I would say it was a success, in that it works - now it just needs some tuning. Then I'll strip it down, repaint and reassemble with the bolts locked down." -- You've got a lot to be proud of. Your kart looks great. Your issues are all fixable. I bet next time you build, you'll wait until the kart's done before you paint...live and learn!
Sean