Hi there,
Hardly the right forum to ask this sort of question, but there we are!!
Anyway.....Your total load is only about 15 Amps, so if you add a bit for the other lights etc, i doubt you will ever exceed 20 Amps, so only a small isolator is needed.
The problem you have is keeping the battery charged... You cannot get more out than you put in. I do not know what size alternator your scooter has, but it will be struggling to run the extra fog lights...
They will work for a bit, but say your scooter can put out 10 amps, [and i doubt it will] where are you going to get the other 10??
The "9 Amp" part of the battery spec is its amp/hour rating. It should in theory [but will not in practice] put out 9 amps for an hour until it runs down to about 1.8 volts per cell i think it is from memory...
So,
1, An isolator that can handle 20 amps will be fine, [assuming the thing does not have to handle the current for an electric starter]
2, The lights will run for about half an hour until your battery runs down.
3, Fit the biggest capacity battery that you can get to fit in the battery holder.
How are you going to work the lights?? You will not just be able to connect them to the headlight circuit, as it was only designed to run one light and not three, so it will either overheat the switch or the wiring or both and blow any fuses that the scooter may or may not have.
I am not trying to be miserable here, but you are asking your little scooter to run an awful lot of lights!!!
The best thing you could do, is to ask your question on a motorbike forum, someone there might have experience of doing the same as you and be able to help you more. Everyone on here wires houses and factories, not motorbikes!!!
john