I have ridden, at times, with patched tubes that never gave me a problem. Then again, it's just another something to fail. What I do now days, is patch the tube, throw it in my tool box, then put a fresh one in the wheel. It's always good to have an extra tube to throw in your pack for a long ride.
As far as the stator, I don't think a puller is the best way to get that thing off. The correct tool would be best, but if you wanted to order/buy the tool, you wouldn't have gone to harbor freight. This is what I did, and I know other people have done the same...
The thread on your rear axle is the same as the inside of the stator. Thread it in pretty tight, then give it a good whack with a hammer. The axle should tighten down a little more now. Give it another good whack. A couple of repetitions and it should fall right off. I held my stator w/ a strap wrench from HF to tighten the axle in, but I don't think that's necessary. I think as tight as you could get it holding w/ a glove on, would work.
After removing the starter gears and clutch, I also plugged the oil passage from the stator area into the crankcase with Yamabond (just the gasket sealer I use). That way when you time it, you wont be spraying oil everywhere when the cover's off. Just make sure you don't use something that could potentially break apart or fall into your crankcase and cause problems.