I don't have anything to add regarding removal of the back tire, but I'd recommend you have someone do it for you (a bicycle shop should be able to take care of it) and perhaps you could watch them do it for future reference.
One thing i've learned from this forum is that mopeds tend to vibrate a lot when you're riding them, so it's a good idea to get in the habit of checking things like screws and cables and whatnot on a regular basis to see if anything has come loose. It's not a defect of the 'ped. Another thing is to check the air pressure in both tires maybe once a week or so. Get to know your 'ped and how it runs and sounds.
One more thing, follow the manufacturer's recommendations regarding the break-in period. Very important.
Have fun & happy riding!