Might be a ZA50 based on the wheels and model number, hard to say with that picture and the aftermarket color scheme, could be either one. Post a pic of the other side of the bike or let us know if you're running a one speed or 2 speed motor.
I don't think your acceleration problems are due to your transmission fluid. That and your lack of idle once warmed up points to poor carb tuning or air leaks usually. You're leaving the choke OFF right? (pull tab is all the way up, not pressed in?) Have you adjusted your idle screw on the carb in at all? If you can get it to idle you can at least check for basic airleaks