From memory (few years since we've been away) we always got separate insurance as it was cheaper plus I was going a few places a year so it made more sense to have a catch all policy. Questor insurance from looking through my old documents and it was £40 for a years' cover on multiple trips. Needed it too as I kerbed an alloy on a brand new Fiat 500 - claims process was no hassle. Having pre-arranged also helped fend off all the upsell from the car rental firm when you go to pick up.
I won't advise on much more other than to say driving in Paphos I found to be full of what I call "creepers". Driving along the main coastal road up to Coral Bay, everyone waiting at give way junctions coming onto the road would slowly creep onto the main road regardless of if you were there or not. So what should a straight drive always ended up being somewhat of a slalom event, particularly in the main urban areas. It's not like the traffic was ever that bad from memory, so no need to try and force your way out, it just seems the thing for locals to do IME. Having said that, for a small island I found overall the driving to be relatively easy. We went up into the mountains and all around the coast and it was much easier than the Amalfi coast or the towns of Tuscany for example.
