Iceland is not very densely populated, and once you’re out of Reykjavík you can expect the roads to be very quiet if not deserted. The main ring road, which you're likely to spend a lot of time on if you're touring extensively, is paved and of good quality.
If you are staying close to Reykjavik and the Golden Circle, which connects the main attractions of the south-west, you are unlikely to come across gravel roads. If, however, you are seeing more of Iceland, gravel surfaces are more common. Slow down, especially when passing others, and you'll be fine.
It's worth taking the extra insurance for damage caused by gravel if you are going further than Reykjavik, the Golden Circle and the other attractions of the south west.
It's also worth noting that hire cars are prohibited on F roads, which are usually extremely rough and in the mountains. Don't panic, these are clearly marked both on the map you'll be given and at the roadside – you can't end up on one by accident.
Finding somewhere to park in Iceland is simple. You can normally park on the side of the road if there are no markings to tell you otherwise. It’s also usually free of charge, other than in busier areas like the centre of Reykjavík, where you might spot parking meters or parking garages.