Your sputtering and neutral issues are common. All of us seem to have had them from the get go.I still do on occasion.I notice that I can shift to neutral on the down shift while the bike is slowly rolling to a stop..so it is now second nature to do so coming up on traffic stops.The sputtering well.. I just ignore it..it goes away as I ride most of the time. Remember these are cheap rides, and you get what you pay for.I have just under 11,000 miles on mine at this time, and with it being riding season now...well the numbers are most definetly going to increase.
I know alot of folks on here have done some adjusting,tweeking, and overall mods...I kept mine basic stock from the wrapper.Just swapped out the bars for mini ape hangers, and added saddle bags( had to fabricate the brackets). also after many rides, I eventually had to change the seat. Aside from that she is bone stock, and runs just like I want her to. Heck I have not even changed the spark plug yet. But I know now that i said something I may have to..murphy's law ya know.
What i am getting at is do not sweat the small stuff.. it is what it is.
Enjoy the ride, that is what matters. By the way, I have just about any and every tool I need to basically rebuild the bike ,all in two neat little tool bags that are always in my saddle bags...ya never know.