Moped Army

Folks, I have an odd problem I am trying to diagnose. I have a 1998 Zuma II. When I first start it up and go WOT it pulls like a Yamaha scooter should (I own several of similar make and year). But, it shifts into the next gear too early, way before my other Yamaha's would shift, and then I completely lose all of my acceleration because the engine RPMs are so low. In addition to this, when I bring the bike to a complete stop it does not go back into the first gear. If I go WOT it will barely accelerate at all. At this point, if on a straight road, it will get up to 30mph like it should, but it never shifts and it takes a LONG time to get there. If I turn the bike off and engage the starter to turn it back on, I am now back in my 1st gear and I am back to square 1. Basically two issues, and I'm trying to figure out how they are related:
1) shifts too early
2) wont automatically shift back to 1st when I stop