[Mech]

I presume that by self tightening nuts you mean Nylock nuts.
Nylock nuts don't need lock-washers.
All nuts, and bolts, whether nylock or not, should have a flat washer. There should generally be a spring washer for non-nylock nuts or bolts.

Wheel nuts, the ones that hold the wheel to the bike, are not normally nylock nuts. If they are a flat nut, not a taper seat nut like a car has, generally have a flat washer and a nut. I've never seen a quad with lock washers on the wheel nuts.
The nylock nuts are likely to be engine mount nuts, or for something on the suspension.

 

[Mech]

10mm bolts are quite large for something like that. Could they be spare wheel bolts. Maybe they do intend it to have lock-washers on the wheels.

Hang onto them, a place will no doubt show up eventually..

 

[Mech]

Ah. I should have guessed that.. haha.

So you had to fit the handlebars, wheels, and carrier racks ? Is that all ?

 

[Mech]

Ha.. Ok. That is shite alright.. Good of them to suggest it's your fault for not getting them to assemble it, but then, that they don't know where things go !! Who'd want to pay them to take guesses ?

It could be that there'd be a bolt or washer to spare, but it seems a bit strange they are in sets of six. Don't know why the lock washers would be spare though. Keep looking, you'll spot it eventually.

 

[Mech]

And giving it a run for an hour or so and then going over it checking everything's tight will be a good idea... It's always a good idea.

 

[Mech]

Belt drive ? And that part was all pre-assembled by them ?
Check the brakes aren't dragging. Lift the rear wheel off the ground(leaning it over on it's side stand will lift the wheel), and letting it run the wheel around for a few minutes with no load letting the belt settle/bed in.

Does it have an owners manual ? Have you checked there isn't some power/throttle limiting device/setting in place to make it safe for novices ?

 

[Mech]

Yeah a tight brake could drag the power. Drum brakes always have an adjustment of some sort. Loosen off the cable adjuster at the bars first. Then if you look at the back of the drum there should be a cable adjustment, try backing that off if the bars adjuster wasn't enough. That might be all it needs. On the back of the drum there might be some sort of adjuster too, it might be a lug for a spanner to turn, or it might have a rubber bung in a hole. Have a look for anything like that and let me know if the cable adjustment didn't get the wheel turning freely. We might need to adjust that.

The other thing is the belt drive is a variable ration and it might be stuck in a high ratio at the moment because it's new and has perhaps been sitting around. I'd get the back wheel off the ground and run it at different speeds for a few minutes. I'd give it a good rev to free up any stuck weights in the centrifugal mechanism that causes the ratio changes.