Modern Vespa

Hey so I bought a 2007 fly 125 a couple of months ago from a private seller. I have a few start-up issues and it is due for rego in a month. Any ideas what the problem might be ? I would like to spend as little money as possible getting it passed by a mechanic, but I know it will need work on how it starts.
My fuel economy is ok, 200km per tank roughly.
Also, horn only works when throttle is in a specific spot and im not sure weather it is a loose connection or just the horn needs to be replaced.

Any help would be great.

Horn issue?
Could it be a dying battery and you need just the right voltage generated by the engine to make it go beep?
If there is not enough voltage there is not enough horn.
Could also be part of starting issue?
Start with the easy things first...

the throttle has to be at the lowest acceleration point, I am almost certain the battery has never been replaced since new. Could this be most likely problem?