Wet weather running issues.

Hi all this is my first post so I hope I've posted in the right place.
Peugeot speedfight 2 AC 50cc
Model wrc 206
Year 2002
Issue wet weather running,limited revs on warm up.
So my son bought this moped just before Christmas and from the start he had starting issues but eventually it did start so he swap out the battery for a new one and the sparkplug which did improve things but it was still hit and miss whether it would start on the electric start or the kickstart.
So forward a month or so then the rain came and caused more problems,the bike was stored outside under what we thought was a waterproof cover but it turns out it was only let's say splashproof.
What we found was that the bike was sweeting under the cover and causing condensation to build up in the warning lights and maybe elsewhere but when you tried to start it you had no chance so I put the bike in my workshop with a heater on for a few hrs then the bike would start and the condensation had gone from the waring lights.
Now if the bike was stored in a dry place but then rode in wet weather the bike would struggle and on occasion cut out but eventually start again and this became a daily occurrence if ride in wet weather.
I will attach some photos of the bike showing the sparkplug area,now I think there's a plastic cover missing around the sparkplug/rear mudguard area but I could be wrong plus I think there should be a rubber disc missing that attaches to the supresseor cap,also some wires showing and a connector not attached to anything.
Now I asked my son to check all this which he said he'd done but obviously not so I'm hoping you good people on here might be able to point me in the right direction before I start checking other things.

 

Sorry forgot to add the extra photos

 

Yes it looks like the splash cover is missing so water off rear wheel is going onto spark plug, get some wd40 and spray all over electrical components and get a splash guard. warn reeds could be a reason for poor starting ?

 

Hi Marsh thanks again for replying to my message.
Could you have a look at these photis

 

Ment to say have a look at these photo's and tell me if this is the right one.
Cheers kev

 

Looks like that's for the front.
Struggling to find the rear piece.

 

The rear splash cover is basically a sheet rubber that just hangs down between wheel and cylinder.

 

Yeah just found that out bit thanks again for telling me I'll get the son to find a rubber mat and get on with it.
Cheers kev

 

But not bit