Help with Peugeot Vivacity 3

[Mw2299]

Hi guys. I'm a new scooter rider.

I just got my bike a few days ago and paid £350 for it. I personally think it was a good price for a 7 year old Peugeot Vivacity 3 50cc with just under 14,000 miles on the clock. It's in brilliant condition with just some age related marks here and there, but nothing major.

I have every MOT paper since birth and it's always passed. Only ever had one advisory which was the brake pads, which have been replaced. To the previous owner's own avail, they also replaced the stock exhaust with a Tecnigas exhaust and have also fitted new rollers. I believe the reasoning for replacing the exhaust is because it was a bit rusty. No idea about the rollers though.

On the downside, I'm having a few, what I assume are, minor issues.

1) Sometimes, but not always, when I pull my throttle all the way back it will just crawl along at a ridiculously slow speed (like 5/10mph) and then picks up speed all of a sudden. It's not only annoying but also dangerous when I'm idle at a set of traffic lights or junction and then my bike just sits there for ages before actually getting anywhere.

2) I don't know if this is in relation to the above issue or not so I'll list it as a separate one. When I'm riding, the speed that the bike wants to go is very temperamental. I don't mean just a few mph because of hills or wind. For example, I'll get up to 30ish and then my bike will slowly start losing speed. I release the throttle and/or pull over and then get going again. Again, frustrating as hell. As well as this, it will sometimes just stay at 30mph and then other times it'll happily go to 40mph according to my bike's speedo. I'm still restricted, according to the previous owners, and I need to cut the CDI cable and do something in the variator to derestrict. Apparently the exhaust doesn't need touching as it has no restricter in it.

3) Finally, my back break is a little sticky. I pull it and then it goes back about half way so I have to push it back into place. Anyone know how to go about fixing this?

Cheers people!